Systems and methods for mask-based temporal dithering

ABSTRACT

In one embodiment, a computing system may determine that a target grayscale value for a frame falls within a predetermined grayscale range. The system may compute, based on the target grayscale value, barycentric weights for a predetermined barycentric coordinate system associated with vertices that each represents a subframe combination of zero or more subframe identifiers. The system select, using the barycentric weights and threshold values associated with respective dots in a dithering mask, a set of non-overlapping dot patterns from the dithering mask corresponding to the vertices of the barycentric coordinate system. The dots in the dithering mask may satisfy a spatial stacking constraint. The system may generate subframes to represent the frame based on the set of non-overlapping dot patterns and the subframe combination represented by each of the vertices.

TECHNICAL FIELD

This disclosure generally relates to artificial reality, such as virtualreality and augmented reality.

BACKGROUND

Artificial reality is a form of reality that has been adjusted in somemanner before presentation to a user, which may include, e.g., a virtualreality (VR), an augmented reality (AR), a mixed reality (MR), a hybridreality, or some combination and/or derivatives thereof. Artificialreality content may include completely generated content or generatedcontent combined with captured content (e.g., real-world photographs).The artificial reality content may include video, audio, hapticfeedback, or some combination thereof, and any of which may be presentedin a single channel or in multiple channels (such as stereo video thatproduces a three-dimensional effect to the viewer). Artificial realitymay be associated with applications, products, accessories, services, orsome combination thereof, that are, e.g., used to create content in anartificial reality and/or used in (e.g., perform activities in) anartificial reality. The artificial reality system that provides theartificial reality content may be implemented on various platforms,including a head-mounted display (HMD) connected to a host computersystem, a standalone HMD, a mobile device or computing system, or anyother hardware platform capable of providing artificial reality contentto one or more viewers.

SUMMARY OF PARTICULAR EMBODIMENTS

Particular embodiments described herein relate to a method of generatingthree subframes based on a dithering mask and a set of barycentriccoordinate systems to represent a target image. As an example and not byway of limitation, the method may use a unit cube's eight vertices torepresent the three subframes (S1, S2, S3) and combinations of zero ormore subframes (no subframes, S1+S2, S1+S3, S2+S3, S1+S2+S3). It isnotable that the subframe combinations herein are for example purposeonly and the systems, methods, and processes described in thisdisclosure are not limited thereto. The subframe combinations may be anysuitable combinations in any suitable orders. For example, the systems,methods, and processes are still applicable if one or more of thesubframes (e.g., S1, S2, S3) are swapped. The unit cube may be dividedinto six tetrahedrons, four of which may be used for determining thebarycentric coordinate systems for generating the subframes. For atarget grayscale value (e.g., an average grayscale value of a tileregion in a target image), the system may first determine which of thetetrahedrons (e.g., one of the four tetrahedrons for determining thebarycentric coordinate system) the grayscale value falls in based on thethreshold ranges associated with the tetrahedrons. Then, the system maydetermine a weight vector (including the barycentric weights) and avertex vector (including combination of subframe identifiers) based onthe associated tetrahedron which the grayscale value falls in. Afterthat, the system may determine four non-overlapping dot sets of thedither mask (e.g., a blue-noise dithering mask) corresponding to thefour barycentric weight values of the weight vector. At last, the systemmay determine the dot sets that are to be turned on or included in eachof the three subframes based on the four non-overlapping dot sets of thedithering mask and a set of rules for assigning dots to the subframes.As a result, the system may generate three subframes satisfying aspatial-stacking property as determined by the dithering mask.

For a target image having a larger size than the dithering mask, thedithering mask may be replicated to cover the target image. To determinein which subframe(s) a given dot of the dithering mask should beincluded, the system may first determine the dithering mask thresholdvalue Q associated with that dot based on a replicated mask coveringthat region of the target image. Then, the system may compare thedithering mask threshold value Q to the cumulative sum of thebarycentric weights of the target grayscale value with respect to theassociated tetrahedron. The system may select a tetrahedron vertex basedon the result of the comparison. The selected tetrahedron vertex may beassociated with a combination of zero or more subframe identifiers.

In particular embodiments, the system may first receive a target pixelvalue p which could be an average pixel value of a target region of atarget image. The target pixel value p may be normalized to a range of[0, 1]. The system may first determine which range the target pixelvalue p falls within among the four value ranges of 0≤p<⅓, ⅓≤p<½, ½≤p<⅔,and ⅔≤p≤1. When the target pixel value p falls within the value range of0≤p<⅓, the system may select a first tetrahedron of a unit cube fordetermining a barycentric coordinate system. The selected tetrahedronmay have its vertices being associated with subframe identifiers of[OFF, S1, S2, S3]. The system may determine the barycentric weights forthe target pixel value p with respect to the selected tetrahedron usinga weight vector w=[1−3p, p, p, p]. Then, the system may determine fournon-overlapping dot sets of the dithering mask based on the fourbarycentric weight values of 1−3p, p, p, and p of the weight vector w.For example, the system may determine a first dot set A1 including dotsin the dithering mask having threshold values below the mask thresholdof 1−3p, a second dot set B1 including dots in the dithering mask havingthreshold values between the thresholds of 1−3p and (1−3p)+p, a thirddot set C1 including dots in the dithering mask having threshold valuesbetween the thresholds of (1−3p)+p, and (1−3p)+p+p, and a fourth dot setD1 including dots in the dithering mask having threshold values betweenthe thresholds of (1−3p)+p+p, and 1. Each dot set of the fournon-overlapping dot sets may include a percentage of dots of the totaldots in the mask corresponding to a barycentric weight value of thetarget pixel value. After that, the system may assign the dots to thesubframes by: (1) excluding dots in the first dot set A1 from any of thethree subframes; and (2) including dots in the second dot set B1 in thefirst subframe S1; (3) including dots in the third dot set C1 in thesecond subframe S2; and (4) including dots on the fourth dot set D1 inthe third subframe S3. As a result, the three subframes may satisfy thespatial stacking property by each including a non-overlapping dot setand not sharing any dots with other subframes.

When the target pixel value p falls within the value range of ⅓≤p<½, thesystem may select a second tetrahedron of the unit cube for determininga barycentric coordinate system. The selected tetrahedron may have itsvertices being associated with subframe identifiers of [S1, S2, S3,S1+3]. The system may determine the barycentric weights for the targetpixel value p with respect to the selected tetrahedron using a weightvector of w=[1−2p, p, 1−2p, 3p−1]. Then, the system may determine fournon-overlapping dot sets of the dithering mask based on the fourbarycentric weight values of 1−2p, p, 1−2p, and 3p−1 of the weightvector w. For example, the system may determine a first dot set A2including dots in the dithering mask having threshold values below themask threshold of 1−2p, a second dot set B2 including dots in thedithering mask having threshold values in the range of [1−2p, (1−2p)+p],a third dot set C2 including dots in the dithering mask having thresholdvalues on the range of [(1−2p)+p, (1−2p)+p+(1−2p)], and a fourth dot setD2 including dots in the dithering mask having threshold values in therange of [(1−2p)+p+(1−2p), 1]. Each dot set of the four non-overlappingdot sets may include a percentage of dots of the total dots in the maskcorresponding to a barycentric weight value of the target pixel value.After that, the system may assign the dot sets to the subframes by: (1)including on the first dot set A2 in the first subframe S1; (2)including the second dot set B2 in the second subframe S2; (3) includingthe third dot set C2 in the third subframe S3; and (4) including thefourth dot set D2 in both the first subframe S1 and the third subframeS3. As a result, the three subframes may include dot sets satisfying thespatial stacking property as determined by the dithering mask.

When the target pixel value p falls within the value range of ½≤p<⅔, thesystem may select a third tetrahedron of the unit cube for determiningthe barycentric coordinate system. The selected tetrahedron may have itsvertices being associated with the subframe identifiers of [ S1+S3,S2+S3, S2, S1+S2]. The system may determine the barycentric weights forthe target pixel value p with respect to the selected tetrahedron usinga weight vector w=[2p−1, 2p−1, 2−3p, 1−p]. Then, the system maydetermine four non-overlapping dot sets of the dithering mask based onthe four weight values of 2p−1, 2p−1, 2−3p, and 1−p of the weight vectorw. For example, the system may determine a first dot set A3 includingdots in the dithering mask having threshold values below the maskthreshold of 2p−1, a second dot set B3 including dots in the ditheringmask having threshold values in the range of [2p−1, (2p−1)+(2p−1)], athird dot set C3 including dots in the dithering mask having thresholdvalues in the range of [(2p−1)+(2p−1), (2p−1)+(2p−1)+(2−3p)], and afourth dot set D3 including dots in the dithering mask having thresholdvalues in the range of [(2p−1)+(2p−1)+(2−3p), 1]. Each dot set of thefour non-overlapping dot sets may include a percentage of dots of thetotal dots in the mask corresponding to a weight value of the weightvector. After that, the system may assign the dot sets to the subframesby: (1) including the first dot set A3 in the first and third subframes(S1+S3); (2) including the second dot set B3 in the second and thirdsubframes (S2+S3); (3) including the third dot set C3 in the secondsubframe S2; and (4) including the fourth dot set D3 in both the firstand second subframe (S1+S2). As a result, the three subframes mayinclude dot sets satisfying the spatial stacking property as determinedby the dithering mask.

When the target pixel value p falls within the value range of ⅔≤p≤1, thesystem may determine select a fourth tetrahedron of the unit cube fordetermining the barycentric coordinate system. The selected tetrahedronmay have its vertices being associated with subframe identifiers of[S1+S3, S2+S3, S1+S2, S1+S2+S3]. The system may determine thebarycentric weights for the target pixel value p with respect to theselected tetrahedron using a weight vector using w=[1−p, 1−p, 1−p,3p−2]. Then, the system may determine four non-overlapping dot sets ofthe dithering mask based on the four weight values of 1−p, 1−p, 1−p, and3p−2 of the weight vector w. For example, the system may determine afirst dot set A4 including dots in the dithering mask having thresholdvalue below a mask threshold of 1−p, a second dot set B4 including dotsin the dithering mask having threshold values in the range of [1−p,(1−p)+(1−p)], a third dot set C4 including dots in the dithering maskhaving threshold value in the range of [(1−p)+(1−p), (1−p)+(1−p)+(1−p)],and a fourth dot set D4 including dots in the dithering mask havingthreshold values in the range of [(1−p)+(1−p)+(1−p), 1]. Each dot set ofthe four non-overlapping dot sets may include a percentage of dots ofthe total dots in the mask corresponding to a barycentric weight valueof the weight vector. After that, the system may assign the dot sets tothe subframes by: (1) including the first dot set A4 in the first andthird subframes (S1+S3); (2) including the second dot set B4 in thesecond and third subframes (S2+S3); (3) including the third dot set C4in the first and second subframe S1+S2; and (4) including the fourth dotset D4 in the first, second, and third subframes (S1+S2+S3). As aresult, the three subframes may include dot sets satisfying the spatialstacking property as determined by the dithering mask.

The embodiments disclosed herein are only examples, and the scope ofthis disclosure is not limited to them. Particular embodiments mayinclude all, some, or none of the components, elements, features,functions, operations, or steps of the embodiments disclosed above.Embodiments according to the invention are in particular disclosed inthe attached claims directed to a method, a storage medium, a system anda computer program product, wherein any feature mentioned in one claimcategory, e.g. method, can be claimed in another claim category, e.g.system, as well. The dependencies or references back in the attachedclaims are chosen for formal reasons only. However, any subject matterresulting from a deliberate reference back to any previous claims (inparticular multiple dependencies) can be claimed as well, so that anycombination of claims and the features thereof are disclosed and can beclaimed regardless of the dependencies chosen in the attached claims.The subject-matter which can be claimed comprises not only thecombinations of features as set out in the attached claims but also anyother combination of features in the claims, wherein each featurementioned in the claims can be combined with any other feature orcombination of other features in the claims. Furthermore, any of theembodiments and features described or depicted herein can be claimed ina separate claim and/or in any combination with any embodiment orfeature described or depicted herein or with any of the features of theattached claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an example artificial reality system.

FIG. 1B illustrates an example augmented reality system.

FIG. 1C illustrates an example architecture of a display engine.

FIG. 1D illustrates an example graphic pipeline of the display enginefor generating display image data.

FIG. 2A illustrates an example scanning waveguide display.

FIG. 2B illustrates an example scanning operation of the scanningwaveguide display.

FIG. 3A illustrates an example 2D micro-LED waveguide display.

FIG. 3B illustrates an example waveguide configuration for the 2Dmicro-LED waveguide display.

FIG. 4A illustrates an example target image to be represented by aseries of subframe images with less color depth.

FIGS. 4B-D illustrate example subframe images generated using segmentedquantization and spatio dithering method to represent the target imageof FIG. 4A.

FIG. 5A illustrates an example dithering mask based on dot patterns withblue-noise properties and satisfying spatio stacking constraints.

FIGS. 5B-D illustrate example dot patterns for grayscale level 1, 8, and32 in a grayscale level range of [0, 255].

FIG. 6 illustrates an example unit cube for determining barycentriccoordinate systems based on respective tetrahedrons of the unit cube.

FIG. 7 illustrates an example method for generating a number ofsubframes based on a barycentric coordinate system and a dithering maskfor representing a target frame.

FIG. 8 illustrates an example computer system.

DESCRIPTION OF EXAMPLE EMBODIMENTS

The number of available bits in a display may limit the display's colordepth or gray scale level. To achieve display results with highereffective grayscale level, displays may use a series of temporalsubframes with less grayscale level bits to create the illusion of atarget image with more grayscale level bits. However, subframes withnaïve stacking property (e.g., direct stacking property without using adithering mask) and unequal weights (e.g., determined by segmentedquantization) may have artifacts (e.g., flashing and uneven luminancebetween different subframes) which may negatively impact the experienceof the viewers. Furthermore, the dithering methods using a frame bufferfor propagating errors to subsequent subframes may require extra memoryspace to be used as the frame buffer and need more memory resources.

In particular embodiments, the system may use a barycentric coordinatesystem and a dithering mask to generate a series of subframe images forrepresenting a target image. The dithering mask may include a number ofdot patterns with each dot pattern having a dot density corresponding toa grayscale level within the quantization range (e.g., 0-255 grayscalelevels for 8-bit display). The dot patterns may be generated based onblue-noise distribution and satisfy spatial stacking property. Forexample, the dot pattern for grayscale level N may include the dotpatterns for all lower grayscale levels from 0 to N−1. The ditheringmask may include the dot patterns corresponding to all grayscale levelsof the quantization range. Each dot in the dithering mask may correspondto a threshold value which equals to the lowest grayscale level allowingthat dot to be included in a dot pattern. For a target pixel value, thesystem may determine a barycentric coordinate system based on atetrahedron of a unit cube that the target pixel value falls in. Thesystem may determine the barycentric weights for the target pixel valuewith respect to the barycentric coordinate system. The vertices of thebarycentric coordinate system may represent combinations of zero or moresubframe identifiers. The system may use the barycentric weights andthreshold values associated with dots in the dithering mask to select aset of non-overlapping dot patterns. The system may generate a number ofsubframes based on the non-overlapping dot patterns and the combinationsof the subframe identifier represented by the vertices of thebarycentric coordinate system.

Particular embodiments of the system provide better image quality andimprove user experience for AR/VR display by using multiple subframeimages with less color depth to represent an image with greater colordepth. Particular embodiments of the system generate subframe image withreduced or eliminated temporal artifacts such as flashes. Particularembodiments of the system improve the efficiency of AR/VR display byreducing the memory usage related to generating the temporal subframeimages by using a dithering mask without using an error buffer.Particular embodiments of the system allow AR/VR display system toreduce the space and complexity of pixel circuits by having less graylevel bits, and therefore miniaturize the size of the display system.Particular embodiments of the system make it possible for AR/VR displaysto operate in monochrome mode with digital pixel circuits without usinganalog pixel circuits for full RGB operations.

FIG. 1A illustrates an example artificial reality system 100A. Inparticular embodiments, the artificial reality system 100 may comprise aheadset 104, a controller 106, and a computing system 108. A user 102may wear the headset 104 that may display visual artificial realitycontent to the user 102. The headset 104 may include an audio devicethat may provide audio artificial reality content to the user 102. Theheadset 104 may include one or more cameras which can capture images andvideos of environments. The headset 104 may include an eye trackingsystem to determine the vergence distance of the user 102. The headset104 may be referred as a head-mounted display (HDM). The controller 106may comprise a trackpad and one or more buttons. The controller 106 mayreceive inputs from the user 102 and relay the inputs to the computingsystem 108. The controller 206 may also provide haptic feedback to theuser 102. The computing system 108 may be connected to the headset 104and the controller 106 through cables or wireless connections. Thecomputing system 108 may control the headset 104 and the controller 106to provide the artificial reality content to and receive inputs from theuser 102. The computing system 108 may be a standalone host computersystem, an on-board computer system integrated with the headset 104, amobile device, or any other hardware platform capable of providingartificial reality content to and receiving inputs from the user 102.

FIG. 1B illustrates an example augmented reality system 100B. Theaugmented reality system 100B may include a head-mounted display (HMD)110 (e.g., glasses) comprising a frame 112, one or more displays 114,and a computing system 120. The displays 114 may be transparent ortranslucent allowing a user wearing the HMD 110 to look through thedisplays 114 to see the real world and displaying visual artificialreality content to the user at the same time. The HMD 110 may include anaudio device that may provide audio artificial reality content to users.The HMD 110 may include one or more cameras which can capture images andvideos of environments. The HMD 110 may include an eye tracking systemto track the vergence movement of the user wearing the HMD 110. Theaugmented reality system 100B may further include a controllercomprising a trackpad and one or more buttons. The controller mayreceive inputs from users and relay the inputs to the computing system120. The controller may also provide haptic feedback to users. Thecomputing system 120 may be connected to the HMD 110 and the controllerthrough cables or wireless connections. The computing system 120 maycontrol the HMD 110 and the controller to provide the augmented realitycontent to and receive inputs from users. The computing system 120 maybe a standalone host computer system, an on-board computer systemintegrated with the HMD 110, a mobile device, or any other hardwareplatform capable of providing artificial reality content to andreceiving inputs from users.

FIG. 1C illustrates an example architecture 100C of a display engine130. In particular embodiments, the processes and methods as describedin this disclosure may be embodied or implemented within a displayengine 130 (e.g., in the display block 135). The display engine 130 mayinclude, for example, but is not limited to, a texture memory 132, atransform block 133, a pixel block 134, a display block 135, input databus 131, output data bus 142, etc. In particular embodiments, thedisplay engine 130 may include one or more graphic pipelines forgenerating images to be rendered on the display. For example, thedisplay engine may use the graphic pipeline(s) to generate a series ofsubframe images based on a mainframe image and a viewpoint or view angleof the user as measured by one or more eye tracking sensors. Themainframe image may be generated or/and loaded in to the system at amainframe rate of 30-90 Hz and the subframe rate may be generated at asubframe rate of 1-2 kHz. In particular embodiments, the display engine130 may include two graphic pipelines for the user's left and righteyes. One of the graphic pipelines may include or may be implemented onthe texture memory 132, the transform block 133, the pixel block 134,the display block 135, etc. The display engine 130 may include anotherset of transform block, pixel block, and display block for the othergraphic pipeline. The graphic pipeline(s) may be controlled by acontroller or control block (not shown) of the display engine 130. Inparticular embodiments, the texture memory 132 may be included withinthe control block or may be a memory unit external to the control blockbut local to the display engine 130. One or more of the components ofthe display engine 130 may be configured to communicate via a high-speedbus, shared memory, or any other suitable methods. This communicationmay include transmission of data as well as control signals, interruptsor/and other instructions. For example, the texture memory 132 may beconfigured to receive image data through the input data bus 211. Asanother example, the display block 135 may send the pixel values to thedisplay system 140 through the output data bus 142. In particularembodiments, the display system 140 may include three color channels(e.g., 114A, 114B, 114C) with respective display driver ICs (DDIs) of142A, 142B, and 143B. In particular embodiments, the display system 140may include, for example, but is not limited to, light-emitting diode(LED) displays, organic light-emitting diode (OLED) displays, activematrix organic light-emitting diode (AMLED) displays, liquid crystaldisplay (LCD), micro light-emitting diode (μLED) display,electroluminescent displays (ELDs), or any suitable displays.

In particular embodiments, the display engine 130 may include acontroller block (not shown). The control block may receive data andcontrol packages such as position data and surface information fromcontrollers external to the display engine 130 though one or more databuses. For example, the control block may receive input stream data froma body wearable computing system. The input data stream may include aseries of mainframe images generated at a mainframe rate of 30-90 Hz.The input stream data including the mainframe images may be converted tothe required format and stored into the texture memory 132. Inparticular embodiments, the control block may receive input from thebody wearable computing system and initialize the graphic pipelines inthe display engine to prepare and finalize the image data for renderingon the display. The data and control packets may include informationrelated to, for example, one or more surfaces including texel data,position data, and additional rendering instructions. The control blockmay distribute data as needed to one or more other blocks of the displayengine 130. The control block may initiate the graphic pipelines forprocessing one or more frames to be displayed. In particularembodiments, the graphic pipelines for the two eye display systems mayeach include a control block or share the same control block.

In particular embodiments, the transform block 133 may determine initialvisibility information for surfaces to be displayed in the artificialreality scene. In general, the transform block 133 may cast rays frompixel locations on the screen and produce filter commands (e.g.,filtering based on bilinear or other types of interpolation techniques)to send to the pixel block 134. The transform block 133 may perform raycasting from the current viewpoint of the user (e.g., determined usingthe headset's inertial measurement units, eye tracking sensors, and/orany suitable tracking/localization algorithms, such as simultaneouslocalization and mapping (SLAM)) into the artificial scene wheresurfaces are positioned and may produce tile/surface pairs 144 to sendto the pixel block 134. In particular embodiments, the transform block133 may include a four-stage pipeline as follows. A ray caster may issueray bundles corresponding to arrays of one or more aligned pixels,referred to as tiles (e.g., each tile may include 16×16 aligned pixels).The ray bundles may be warped, before entering the artificial realityscene, according to one or more distortion meshes. The distortion meshesmay be configured to correct geometric distortion effects stemming from,at least, the eye display systems the headset system. The transformblock 133 may determine whether each ray bundle intersects with surfacesin the scene by comparing a bounding box of each tile to bounding boxesfor the surfaces. If a ray bundle does not intersect with an object, itmay be discarded. After the tile-surface intersections are detected, thecorresponding tile/surface pairs may be passed to the pixel block 134.

In particular embodiments, the pixel block 134 may determine colorvalues or grayscale values for the pixels based on the tile-surfacepairs. The color values for each pixel may be sampled from the texeldata of surfaces received and stored in texture memory 132. The pixelblock 134 may receive tile-surface pairs from the transform block 133and may schedule bilinear filtering using one or more filer blocks. Foreach tile-surface pair, the pixel block 134 may sample color informationfor the pixels within the tile using color values corresponding to wherethe projected tile intersects the surface. The pixel block 134 maydetermine pixel values based on the retrieved texels (e.g., usingbilinear interpolation). In particular embodiments, the pixel block 134may process the red, green, and blue color components separately foreach pixel. In particular embodiments, the display may include two pixelblocks for the two eye display systems. The two pixel blocks of the twoeye display systems may work independently and in parallel with eachother. The pixel block 134 may then output its color determinations(e.g., pixels 138) to the display block 135. In particular embodiments,the pixel block 134 may composite two or more surfaces into one surfaceto when the two or more surfaces have overlapping areas. A composedsurface may need less computational resources (e.g., computationalunits, memory, power, etc.) for the resampling process.

In particular embodiments, the display block 135 may receive pixel colorvalues from the pixel block 134, covert the format of the data to bemore suitable for the scanline output of the display, apply one or morebrightness corrections to the pixel color values, and prepare the pixelcolor values for output to the display. In particular embodiments, thedisplay block 135 may each include a row buffer and may process andstore the pixel data received from the pixel block 134. The pixel datamay be organized in quads (e.g., 2×2 pixels per quad) and tiles (e.g.,16×16 pixels per tile). The display block 135 may convert tile-orderpixel color values generated by the pixel block 134 into scanline orrow-order data, which may be required by the physical displays. Thebrightness corrections may include any required brightness correction,gamma mapping, and dithering. The display block 135 may output thecorrected pixel color values directly to the driver of the physicaldisplay (e.g., pupil display) or may output the pixel values to a blockexternal to the display engine 130 in a variety of formats. For example,the eye display systems of the headset system may include additionalhardware or software to further customize backend color processing, tosupport a wider interface to the display, or to optimize display speedor fidelity.

In particular embodiments, the dithering methods and processes (e.g.,spatial dithering method, temporal dithering methods, andspatio-temporal methods) as described in this disclosure may be embodiedor implemented in the display block 135 of the display engine 130. Inparticular embodiments, the display block 135 may include a model-baseddithering algorithm or a dithering model for each color channel and sendthe dithered results of the respective color channels to the respectivedisplay driver ICs (e.g., 142A, 142B, 142C) of display system 140. Inparticular embodiments, before sending the pixel values to therespective display driver ICs (e.g., 142A, 142B, 142C), the displayblock 135 may further include one or more algorithms for correcting, forexample, pixel non-uniformity, LED non-ideality, waveguidenon-uniformity, display defects (e.g., dead pixels), etc.

In particular embodiments, graphics applications (e.g., games, maps,content-providing apps, etc.) may build a scene graph, which is usedtogether with a given view position and point in time to generateprimitives to render on a GPU or display engine. The scene graph maydefine the logical and/or spatial relationship between objects in thescene. In particular embodiments, the display engine 130 may alsogenerate and store a scene graph that is a simplified form of the fullapplication scene graph. The simplified scene graph may be used tospecify the logical and/or spatial relationships between surfaces (e.g.,the primitives rendered by the display engine 130, such asquadrilaterals or contours, defined in 3D space, that have correspondingtextures generated based on the mainframe rendered by the application).Storing a scene graph allows the display engine 130 to render the sceneto multiple display frames and to adjust each element in the scene graphfor the current viewpoint (e.g., head position), the current objectpositions (e.g., they could be moving relative to each other) and otherfactors that change per display frame. In addition, based on the scenegraph, the display engine 130 may also adjust for the geometric andcolor distortion introduced by the display subsystem and then compositethe objects together to generate a frame. Storing a scene graph allowsthe display engine 130 to approximate the result of doing a full renderat the desired high frame rate, while actually running the GPU ordisplay engine 130 at a significantly lower rate.

FIG. 1D illustrates an example graphic pipeline 100D of the displayengine 130 for generating display image data. In particular embodiments,the graphic pipeline 100D may include a visibility step 152, where thedisplay engine 130 may determine the visibility of one or more surfacesreceived from the body wearable computing system. The visibility step152 may be performed by the transform block (e.g., 2133 in FIG. 1C) ofthe display engine 130. The display engine 130 may receive (e.g., by acontrol block or a controller) input data 151 from the body-wearablecomputing system. The input data 151 may include one or more surfaces,texel data, position data, RGB data, and rendering instructions from thebody wearable computing system. The input data 151 may include mainframeimages with 30-90 frames per second (FPS). The main frame image may havecolor depth of, for example, 24 bits per pixel. The display engine 130may process and save the received input data 151 in the texel memory132. The received data may be passed to the transform block 133 whichmay determine the visibility information for surfaces to be displayed.The transform block 133 may cast rays for pixel locations on the screenand produce filter commands (e.g., filtering based on bilinear or othertypes of interpolation techniques) to send to the pixel block 134. Thetransform block 133 may perform ray casting from the current viewpointof the user (e.g., determined using the headset's inertial measurementunits, eye trackers, and/or any suitable tracking/localizationalgorithms, such as simultaneous localization and mapping (SLAM)) intothe artificial scene where surfaces are positioned and producesurface-tile pairs to send to the pixel block 134.

In particular embodiments, the graphic pipeline 100D may include aresampling step 153, where the display engine 130 may determine thecolor values from the tile-surfaces pairs to produce pixel color values.The resampling step 153 may be performed by the pixel block 134 in FIG.1C) of the display engine 130. The pixel block 134 may receivetile-surface pairs from the transform block 133 and may schedulebilinear filtering. For each tile-surface pair, the pixel block 134 maysample color information for the pixels within the tile using colorvalues corresponding to where the projected tile intersects the surface.The pixel block 134 may determine pixel values based on the retrievedtexels (e.g., using bilinear interpolation) and output the determinedpixel values to the respective display block 135.

In particular embodiments, the graphic pipeline 100D may include a bendstep 154, a correction and dithering step 155, a serialization step 156,etc. In particular embodiments, the bend step, correction and ditheringstep, and serialization steps of 154, 155, and 156 may be performed bythe display block (e.g., 135 in FIG. 1C) of the display engine 130. Thedisplay engine 130 may blend the display content for display contentrendering, apply one or more brightness corrections to the pixel colorvalues, perform one or more dithering algorithms for dithering thequantization errors both spatially and temporally, serialize the pixelvalues for scanline output for the physical display, and generate thedisplay data 159 suitable for the display system 140. The display engine130 may send the display data 159 to the display system 140. Inparticular embodiments, the display system 140 may include three displaydriver ICs (e.g., 142A, 142B, 142C) for the pixels of the three colorchannels of RGB (e.g., 144A, 144B, 144C).

FIG. 2A illustrates an example scanning waveguide display 200A. Inparticular embodiments, the head-mounted display (HMD) of the AR/VRsystem may include a near eye display (NED) which may be a scanningwaveguide display 200A. The scanning waveguide display 200A may includea light source assembly 210, an output waveguide 204, a controller 216,etc. The scanning waveguide display 200A may provide images for botheyes or for a single eye. For purposes of illustration, FIG. 3A showsthe scanning waveguide display 200A associated with a single eye 202.Another scanning waveguide display (not shown) may provide image lightto the other eye of the user and the two scanning waveguide displays mayshare one or more components or may be separated. The light sourceassembly 210 may include a light source 212 and an optics system 214.The light source 212 may include an optical component that couldgenerate image light using an array of light emitters. The light source212 may generate image light including, for example, but not limited to,red image light, blue image light, green image light, infra-red imagelight, etc. The optics system 214 may perform a number of opticalprocesses or operations on the image light generated by the light source212. The optical processes or operations performed by the optics systems214 may include, for example, but are not limited to, light focusing,light combining, light conditioning, scanning, etc.

In particular embodiments, the optics system 214 may include a lightcombining assembly, a light conditioning assembly, a scanning mirrorassembly, etc. The light source assembly 210 may generate and output animage light 219 to a coupling element 218 of the output waveguide 204.The output waveguide 204 may be an optical waveguide that could outputimage light to the user eye 202. The output waveguide 204 may receivethe image light 219 at one or more coupling elements 218 and guide thereceived image light to one or more decoupling elements 206. Thecoupling element 218 may be, for example, but is not limited to, adiffraction grating, a holographic grating, any other suitable elementsthat can couple the image light 219 into the output waveguide 204, or acombination thereof. As an example and not by way of limitation, if thecoupling element 350 is a diffraction grating, the pitch of thediffraction grating may be chosen to allow the total internal reflectionto occur and the image light 219 to propagate internally toward thedecoupling element 206. The pitch of the diffraction grating may be inthe range of 300 nm to 600 nm. The decoupling element 206 may decouplethe total internally reflected image light from the output waveguide204. The decoupling element 206 may be, for example, but is not limitedto, a diffraction grating, a holographic grating, any other suitableelement that can decouple image light out of the output waveguide 204,or a combination thereof. As an example and not by way of limitation, ifthe decoupling element 206 is a diffraction grating, the pitch of thediffraction grating may be chosen to cause incident image light to exitthe output waveguide 204. The orientation and position of the imagelight exiting from the output waveguide 204 may be controlled bychanging the orientation and position of the image light 219 enteringthe coupling element 218. The pitch of the diffraction grating may be inthe range of 300 nm to 600 nm.

In particular embodiments, the output waveguide 204 may be composed ofone or more materials that can facilitate total internal reflection ofthe image light 219. The output waveguide 204 may be composed of one ormore materials including, for example, but not limited to, silicon,plastic, glass, polymers, or some combination thereof. The outputwaveguide 204 may have a relatively small form factor. As an example andnot by way of limitation, the output waveguide 204 may be approximately50 mm wide along X-dimension, 30 mm long along Y-dimension and 0.5-1 mmthick along Z-dimension. The controller 216 may control the scanningoperations of the light source assembly 210. The controller 216 maydetermine scanning instructions for the light source assembly 210 basedat least on the one or more display instructions for rendering one ormore images. The display instructions may include an image file (e.g.,bitmap) and may be received from, for example, a console or computer ofthe AR/VR system. Scanning instructions may be used by the light sourceassembly 210 to generate image light 219. The scanning instructions mayinclude, for example, but are not limited to, an image light source type(e.g., monochromatic source, polychromatic source), a scanning rate, ascanning apparatus orientation, one or more illumination parameters, orsome combination thereof. The controller 216 may include a combinationof hardware, software, firmware, or any suitable components supportingthe functionality of the controller 216.

FIG. 2B illustrates an example scanning operation of a scanningwaveguide display 200B. The light source 220 may include an array oflight emitters 222 (as represented by the dots in inset) with multiplerows and columns. The light 223 emitted by the light source 220 mayinclude a set of collimated beams of light emitted by each column oflight emitters 222. Before reaching the mirror 224, the light 223 may beconditioned by different optical devices such as the conditioningassembly (not shown). The mirror 224 may reflect and project the light223 from the light source 220 to the image field 227 by rotating aboutan axis 225 during scanning operations. The mirror 224 may be amicroelectromechanical system (MEMS) mirror or any other suitablemirror. As the mirror 224 rotates about the axis 225, the light 223 maybe projected to a different part of the image field 227, as illustratedby the reflected part of the light 226A in solid lines and the reflectedpart of the light 226B in dash lines.

In particular embodiments, the image field 227 may receive the light226A-B as the mirror 224 rotates about the axis 225 to project the light226A-B in different directions. For example, the image field 227 maycorrespond to a portion of the coupling element 218 or a portion of thedecoupling element 206 in FIG. 2A. In particular embodiments, the imagefield 227 may include a surface of the coupling element 206. The imageformed on the image field 227 may be magnified as light travels throughthe output waveguide 220. In particular embodiments, the image field 227may not include an actual physical structure but include an area towhich the image light is projected to form the images. The image field227 may also be referred to as a scan field. When the light 223 isprojected to an area of the image field 227, the area of the image field227 may be illuminated by the light 223. The image field 227 may includea matrix of pixel locations 229 (represented by the blocks in inset 228)with multiple rows and columns. The pixel location 229 may be spatiallydefined in the area of the image field 227 with a pixel locationcorresponding to a single pixel. In particular embodiments, the pixellocations 229 (or the pixels) in the image field 227 may not includeindividual physical pixel elements. Instead, the pixel locations 229 maybe spatial areas that are defined within the image field 227 and dividethe image field 227 into pixels. The sizes and locations of the pixellocations 229 may depend on the projection of the light 223 from thelight source 220. For example, at a given rotation angle of the mirror224, light beams emitted from the light source 220 may fall on an areaof the image field 227. As such, the sizes and locations of pixellocations 229 of the image field 227 may be defined based on thelocation of each projected light beam. In particular embodiments, apixel location 229 may be subdivided spatially into subpixels (notshown). For example, a pixel location 229 may include a red subpixel, agreen subpixel, and a blue subpixel. The red, green and blue subpixelsmay correspond to respective locations at which one or more red, greenand blue light beams are projected. In this case, the color of a pixelmay be based on the temporal and/or spatial average of the pixel'ssubpixels.

In particular embodiments, the light emitters 222 may illuminate aportion of the image field 227 (e.g., a particular subset of multiplepixel locations 229 on the image field 227) with a particular rotationangle of the mirror 224. In particular embodiment, the light emitters222 may be arranged and spaced such that a light beam from each of thelight emitters 222 is projected on a corresponding pixel location 229.In particular embodiments, the light emitters 222 may include a numberof light-emitting elements (e.g., micro-LEDs) to allow the light beamsfrom a subset of the light emitters 222 to be projected to a same pixellocation 229. In other words, a subset of multiple light emitters 222may collectively illuminate a single pixel location 229 at a time. As anexample and not by way of limitation, a group of light emitter includingeight light-emitting elements may be arranged in a line to illuminate asingle pixel location 229 with the mirror 224 at a given orientationangle.

In particular embodiments, the number of rows and columns of lightemitters 222 of the light source 220 may or may not be the same as thenumber of rows and columns of the pixel locations 229 in the image field227. In particular embodiments, the number of light emitters 222 in arow may be equal to the number of pixel locations 229 in a row of theimage field 227 while the light emitters 222 may have fewer columns thanthe number of pixel locations 229 of the image field 227. In particularembodiments, the light source 220 may have the same number of columns oflight emitters 222 as the number of columns of pixel locations 229 inthe image field 227 but fewer rows. As an example and not by way oflimitation, the light source 220 may have about 1280 columns of lightemitters 222 which may be the same as the number of columns of pixellocations 229 of the image field 227, but only a handful rows of lightemitters 222. The light source 220 may have a first length L1 measuredfrom the first row to the last row of light emitters 222. The imagefield 530 may have a second length L2, measured from the first row(e.g., Row 1) to the last row (e.g., Row P) of the image field 227. TheL2 may be greater than L1 (e.g., L2 is 50 to 10,000 times greater thanL1).

In particular embodiments, the number of rows of pixel locations 229 maybe larger than the number of rows of light emitters 222. The displaydevice 200B may use the mirror 224 to project the light 223 to differentrows of pixels at different time. As the mirror 520 rotates and thelight 223 scans through the image field 227, an image may be formed onthe image field 227. In some embodiments, the light source 220 may alsohas a smaller number of columns than the image field 227. The mirror 224may rotate in two dimensions to fill the image field 227 with light, forexample, using a raster-type scanning process to scan down the rows thenmoving to new columns in the image field 227. A complete cycle ofrotation of the mirror 224 may be referred to as a scanning period whichmay be a predetermined cycle time during which the entire image field227 is completely scanned. The scanning of the image field 227 may bedetermined and controlled by the mirror 224 with the light generation ofthe display device 200B being synchronized with the rotation of themirror 224. As an example and not by way of limitation, the mirror 224may start at an initial position projecting light to Row 1 of the imagefield 227, and rotate to the last position that projects light to Row Pof the image field 227, and then rotate back to the initial positionduring one scanning period. An image (e.g., a frame) may be formed onthe image field 227 per scanning period. The frame rate of the displaydevice 200B may correspond to the number of scanning periods in asecond. As the mirror 224 rotates, the light may scan through the imagefield to form images. The actual color value and light intensity orbrightness of a given pixel location 229 may be a temporal sum of thecolor various light beams illuminating the pixel location during thescanning period. After completing a scanning period, the mirror 224 mayrevert back to the initial position to project light to the first fewrows of the image field 227 with a new set of driving signals being fedto the light emitters 222. The same process may be repeated as themirror 224 rotates in cycles to allow different frames of images to beformed in the scanning field 227.

FIG. 3A illustrates an example 2D micro-LED waveguide display 300A. Inparticular embodiments, the display 300A may include an elongatewaveguide configuration 302 that may be wide or long enough to projectimages to both eyes of a user. The waveguide configuration 302 mayinclude a decoupling area 304 covering both eyes of the user. In orderto provide images to both eyes of the user through the waveguideconfiguration 302, multiple coupling areas 306A-B may be provided in atop surface of the waveguide configuration 302. The coupling areas 306Aand 306B may include multiple coupling elements to receive image lightfrom light emitter array sets 308A and 308B, respectively. Each of theemitter array sets 308A-B may include a number of monochromatic emitterarrays including, for example, but not limited to, a red emitter array,a green emitter array, and a blue emitter array. In particularembodiments, the emitter array sets 308A-B may further include a whiteemitter array or an emitter array emitting other colors or anycombination of any multiple colors. In particular embodiments, thewaveguide configuration 302 may have the emitter array sets 308A and308B covering approximately identical portions of the decoupling area304 as divided by the divider line 309A. In particular embodiments, theemitter array sets 308A and 308B may provide images to the waveguide ofthe waveguide configuration 302 asymmetrically as divided by the dividerline 309B. For example, the emitter array set 308A may provide image tomore than half of the decoupling area 304. In particular embodiments,the emitter array sets 308A and 308B may be arranged at opposite sides(e.g., 180° apart) of the waveguide configuration 302 as shown in FIG.3B. In other embodiments, the emitter array sets 308A and 308B may bearranged at any suitable angles. The waveguide configuration 302 may beplanar or may have a curved cross-sectional shape to better fit to theface/head of a user.

FIG. 3B illustrates an example waveguide configuration 300B for the 2Dmicro-LED waveguide display. In particular embodiments, the waveguideconfiguration 300B may include a projector device 350 coupled to awaveguide 342. The projector device 320 may include a number of lightemitters 352 (e.g., monochromatic emitters) secured to a supportstructure 354 (e.g., a printed circuit board or other suitable supportstructure). The waveguide 342 may be separated from the projector device350 by an air gap having a distance of D1 (e.g., approximately 50 μm toapproximately 500 μm). The monochromatic images projected by theprojector device 350 may pass through the air gap toward the waveguide342. The waveguide 342 may be formed from a glass or plastic material.The waveguide 342 may include a coupling area 330 including a number ofcoupling elements 334A-C for receiving the emitted light from theprojector device 350. The waveguide 342 may include a decoupling areawith a number of decoupling elements 336A on the top surface 318A and anumber of decoupling elements 336B on the bottom surface 318B. The areawithin the waveguide 342 in between the decoupling elements 336A and336B may be referred as a propagation area 310, in which image lightreceived from the projector device 350 and coupled into the waveguide342 by the coupling element 334 may propagate laterally within thewaveguide 342.

The coupling area 330 may include coupling elements (e.g., 334A, 334B,334C) configured and dimensioned to couple light of predeterminedwavelengths (e.g., red, green, blue). When a white light emitter arrayis included in the projector device 350, the portion of the white lightthat falls in the predetermined wavelengths may be coupled by each ofthe coupling elements 334A-C. In particular embodiments, the couplingelements 334A-B may be gratings (e.g., Bragg gratings) dimensioned tocouple a predetermined wavelength of light. In particular embodiments,the gratings of each coupling element may exhibit a separation distancebetween gratings associated with the predetermined wavelength of lightand each coupling element may have different grating separationdistances. Accordingly, each coupling element (e.g., 334A-C) may couplea limited portion of the white light from the white light emitter arrayof the projector device 350 if white light emitter array is included inthe projector device 350. In particular embodiments, each couplingelement (e.g., 334A-C) may have the same grating separation distance. Inparticular embodiments, the coupling elements 334A-C may be or include amultiplexed coupler.

As illustrated in FIG. 3B, a red image 320A, a blue image 320B, and agreen image 320C may be coupled by the coupling elements 334A, 334B,334C, respectively, into the propagation area 310 and may begin totraverse laterally within the waveguide 342. A portion of the light maybe projected out of the waveguide 342 after the light contacts thedecoupling element 336A for one-dimensional pupil replication, and afterthe light contacts both the decoupling elements 336A and 336B fortwo-dimensional pupil replication. In two-dimensional pupil replication,the light may be projected out of the waveguide 342 at locations wherethe pattern of the decoupling element 336A intersects the pattern of thedecoupling element 336B. The portion of the light that is not projectedout of the waveguide 342 by the decoupling element 336A may be reflectedoff the decoupling element 336B. The decoupling element 336B may reflectall incident light back toward the decoupling element 336A. Accordingly,the waveguide 342 may combine the red image 320A, the blue image 320B,and the green image 320C into a polychromatic image instance which maybe referred as a pupil replication 322. The polychromatic pupilreplication 322 may be projected to the user's eyes which may interpretthe pupil replication 322 as a full color image (e.g., an imageincluding colors addition to red, green, and blue). The waveguide 342may produce tens or hundreds of pupil replication 322 or may produce asingle replication 322.

In particular embodiments, the AR/VR system may use scanning waveguidedisplays or 2D micro-LED displays for displaying AR/VR content to users.In order to miniaturize the AR/VR system, the display system may need tominiaturize the space for pixel circuits and may have limited number ofavailable bits for the display. The number of available bits in adisplay may limit the display's color depth or gray scale level, andconsequently limit the quality of the displayed images. Furthermore, thewaveguide displays used for AR/VR systems may have nonuniformity problemcross all display pixels. The compensation operations for pixelnonuniformity may result in loss on image grayscale and further reducethe quality of the displayed images. For example, a waveguide displaywith 8-bit pixels (i.e., 256 gray level) may equivalently have 6-bitpixels (i.e., 64 gray level) after compensation of the nonuniformity(e.g., 8:1 waveguide nonuniformity, 0.1% dead micro-LED pixel, and 20%micro-LED intensity nonuniformity).

To improve the displayed image quality, displays with limited colordepth or gray scale level may use spatio dithering to spreadquantization errors to neighboring pixels and generate the illusion ofincreased color depth or gray scale level. To further increase the colordepth or gray scale level, displays may generate a series of temporalsubframe images with less gray level bits to give the illusion of atarget image which has more gray level bits. Each subframe image may bedithered using spatio dithering techniques within that subframe image.The average of the series of subframe image may correspond to the imageas perceived by the viewer. For example, for display an image with 8-bitpixels (i.e., 256 gray level), the system may use four subframe imageseach having 6-bit pixels (i.e., 64 gray level) to represent the 8-bittarget image. As another example, an image with 8-bit pixels (i.e., 256gray level) may be represented by 16 subframe images each having 4-bitpixels (i.e., 16 gray level). This would allow the display system torender images of more gray level (e.g., 8-bit pixels) with pixelcircuits and supporting hardware for less gray level (e.g., 6-bit pixelsor 4-bit pixels), and therefore reduce the space and size of the displaysystem.

FIG. 4A illustrates an example target image 400A to be represented by aseries of subframe images with less color depth. FIGS. 4B-D illustrateexample subframe images 400B-D generated using segmented quantizationand spatio dithering method to represent the target image 400A of FIG.4A. The target image 400A may have more gray level bits than thephysical display. The subframe images 400B-D may have gray level bitscorresponding to the physical display, which is less than the targetimage 400A, and may be used to represent the target image using the timeaverage as perceived by viewers. To generate each subframe image, thevalue of each pixel in the target image may be quantized according to aseries of segmented value ranges corresponding to the weighted valueranges of the subframe images. Each subframe image may correspond to asegmented portion of the pixel range of the target image. The pixelvalue range of each subframe image may be weighted according to thecorresponding segmented portion of the target image pixel range. As anexample and not by way of limitation, the first, second and thirdsubframes (as shown in FIGS. 4B-D, respectively) may cover the grayscalelevel ranges of [0, ⅓], [⅓, ⅔] and [⅔, 1] in the normalized grayscalelevel range of [0, 1]. Using this temporal stacking property, thetemporal integrated noise related to the rendered images may be reducedby 1/N² where Nis the number of subframe images.

However, using this segmented quantization and spatio dithering method,even though the average luminance of the all subframe images over timeis approximately equal to the target image, the subframes 400B-D mayhave very different luminance, as illustrated in FIGS. 4B-D. Forexample, the subframe image 400B capturing the lower energy bits may bevery bright since most pixel value of the target image 400A may exceedthe maximum pixel value of the subframe 400B. The subframe image 400Dcapturing the high energy bits may be very dim because most of the pixelvalue of the target image 400A may be below the pixel value range of thesubframe 400D. This may work well for traditional displays such asLCD/LED displays since the user eyes do not change dramatically betweenthe subframe images. However, it will create temporal artifacts such asflashes, and will negatively impact the quality of the displayed imagesand user experiences on the AR/VR system.

To solve the artifact problem in the subframe images, a spatio-temporaldithering method may be used to generate a series of subframe images forrepresenting a target image with more even luminance distribution acrossall subframe images. The spatio-temporal dithering method may ditherquantization errors both spatially to neighboring pixels of the samesubframe image and temporally to the corresponding pixel of nextsubframe image of the series of subframe images. The temporally ditheredquantization error of a pixel of a subframe image may be dithered to thecorresponding pixel in the next subframe image of the series of subframeimages in the time domain. However, these dithering methods may need anerror buffer to provide temporal feedback, and therefore use morememory. To reduce the memory usage related to processes of generatingsubframe images, particular embodiments of the system may use adithering mask and a barycentric coordinate system to generate theseries of subframe images for representing a target image without usingan error buffer.

FIG. 5A illustrates an example dithering mask based on dot patterns withblue-noise properties and satisfying spatio stacking constraints. FIGS.5B-D illustrate example dot patterns for grayscale level 1, 8, and 32 inthe grayscale level range of [0, 255]. In particular embodiments, thesystem may generate spatio dithering masks based on dot patterns withblue-noise properties. The dithering mask may include a number of dotpatterns with each dot pattern having a dot density corresponding to agrayscale level within the grayscale level range corresponding to thequantization range. A dot pattern for a higher grayscale level may havea higher dot density than a dot pattern for a lower grayscale level. Thedot patterns may be chosen to have blue-noise properties (e.g., with thefrequency spectrum being blue-noise weighted). The grayscale level rangecorresponding to the quantization range may be determined by the bitlength of the display. For example, an 8-bit display may have agrayscale level range of [0, 255]. As another example, a 6-bit displaymay have a grayscale level range of [0, 63]. As another example, a 4-bitdisplay may have a grayscale level range of [0-15]. In particularembodiments, the dot patterns of the dithering mask may have a spatialstacking property according to which a dot pattern of a grayscale levelN may include all dot patterns of lower grayscale levels from 0 to N−1.For example, the dots in the dot pattern of grayscale level 1 (as shownin FIG. 5A) may be included in the dot pattern of grayscale level 8 (asshown in FIG. 5B) and in the dot pattern of grayscale level 32 (as shownin FIG. 5C). As another example, the dots in the dot pattern ofgrayscale level 8 (as shown in FIG. 5B) may be included in the dotpattern of the grayscale level 32 (as shown in FIG. 5C).

In particular embodiments, each dot in the dithering mask may correspondto a threshold value which equals to the lowest grayscale level allowingthat dot to be turned on (i.e., the lowest grayscale level whosecorresponding dot pattern includes that dot). From the lowest grayscalelevel to the highest grayscale level, once a dot is turned on (i.e.,being included in a dot pattern of a grayscale level), the dot may stayin the turn-on state for all higher grayscale levels (i.e., beingincluded in the dot patterns of all higher grayscale levels). The spatiostacking properties of the dot patterns may allow all dot patterns to beencoded into one dithering mask. In particular embodiments, thedithering mask (e.g., 500A in FIG. 5A) may include all the dot patterns(which are spatially stacked together) corresponding to all grayscalelevels of the quantization range which may correspond to the gray levelbits of the display (e.g., [0, 255] for 8-bit display, [0, 63] for 6-bitdisplay, [0, 15] for 3-bit display). The dithering mask (e.g., 500A inFIG. 5A) may have a third dimension for storing the threshold valuesassociated with the respective dots. In particular embodiments, thethreshold values stored in the dithering mask may be the actualgrayscale level values (e.g., [0, 255] for 8-bit display). In particularembodiments, the threshold values stored in the dithering mask may benormalized grayscale level values (e.g., [0, 1] for any bit display). Inthis case, the threshold values may be determined by the normalizedgrayscale level range of [0, 1] and the number of grayscale levels(e.g., 255 for 8-bit display). For example, for an 8-bit display, thethreshold values could be 0, 1/255, 2/255 . . . 8/255 . . . 32/255 . . .255/255, etc. As another example, for a 3-bit display, the thresholdvalues could be 0, 1/7, 2/7, . . . 7/7, etc.

FIG. 6 illustrates an example unit cube 600 for determining barycentriccoordinate systems based on respective tetrahedrons of the unit cube600. In particular embodiments, the system may use one or morebarycentric coordinate systems each corresponding to a tetrahedron ofthe unit cube 600 for generating subframes to represent a target frame.The unit cube 600 may be partitioned into six tetrahedrons. For a pointR within a tetrahedron, the point R may be represented by a linearcombination of the tetrahedron vertices V=[v₁, v₂, v₃, v₄] andassociated barycentric weights W=[w₁, w₂, w₃, w₄] of that point byR=WV^(T). The six tetrahedrons of the unit cube may each have verticescorresponding to either zero or unity value as determined by the unitcube 600. The barycentric weights of a point within a tetrahedron may bedetermined based on comparison operations using only additions orsubtractions.

In particular embodiments, the system may use the unit cube 600 fordetermining the barycentric coordinate systems based on respectivetetrahedrons of the unit cube 600. The unit cube 600 may have verticeseach being associated with a combination of subframe identifiesincluding zero or more subframe identifiers (e.g., the vertex 610 beingassociated with zero subframe indicator OFF, the vertex 611 beingassociated with a first subframe indicator S1, the vertex 612 beingassociated with a second subframe indicator S2, the vertex 613 beingassociated with a third subframe indicator S3, the vertex 614 beingassociated with an indicator for the first subframe and the secondsubframe S1+S2, the vertex 615 being associated with an indicator forthe first subframe and the third subframe S1+S3, the vertex 616 beingassociated with an indicator for the second subframe and the thirdsubframe S2+S3, the vertex 617 being associated with an indicator forthe first subframe, the second subframe, and the third subframeS1+S2+S3).

In particular embodiments, the unit cube 600 may be portioned into sixtetrahedrons with four of them being used as the barycentric coordinatesystems for generating subframes. As an example and not by way oflimitation, the four tetrahedrons that are used as the barycentriccoordinate systems may include, a first tetrahedron formed by thevertices of 610, 611, 612, and 613 corresponding to the subframeidentifiers of OFF, S1, S2, and S3, respectively, a second tetrahedronformed by the vertices of 611, 612, 613, and 6145 corresponding thesubframe identifier of S1, S2, S3, and S1+S3, respectively, a thirdtetrahedron formed by the vertices of 615, 616, 612, and 614corresponding the subframe identifiers of S1+S3, S2+S3, S2, and S1+S2,respectively, and a fourth tetrahedron formed by the vertices of 615,616, 614, and 617 corresponding to the subframe identifiers of S1+S3,S2+S3, S1+S2, and S1+S2+S3, respectively. In particular embodiments, thesystem may use the tetrahedrons and associated subframe identifiers forgenerating subframes based on a dithering mask having a blue-noiseproperty, as will be described in detail later in this disclosure. Thereason why four of the six tetrahedrons are used as the barycentriccoordinate systems may be explained by a precondition that the temporalsum of the subframes is independent of the subframe ordering. With thisprecondition, the other two tetrahedrons may be included by the fourtetrahedrons that are used as the barycentric coordinate systems. It isnotable that the subframe combinations herein are for example purposeonly and the systems, methods, and processes described in thisdisclosure are not limited thereto. The subframe combinations may be anysuitable combinations in any suitable orders. For example, the systems,methods, and processes are still applicable if one or more of thesubframes (e.g., S1, S2, S3) are swapped. It is notable that the mappingrelations between the subframe combinations and the vertices of thebarycentric coordinate system herein are for example purpose only andare not limited thereto. The mapping relations of the subframecombinations and the vertices of the barycentric coordinate system maybe any suitable mapping relations and the systems, methods, andprocesses as described in this disclosure are applicable.

In particular embodiments, the system may generate a number of subframeswith less grayscale level bits to represent a target image with moregrayscale level bits based on the barycentric coordinate systems asdetermined by the tetrahedrons of a unit cube. As an example and not byway of limitation, the system may generate a set of three subframes forrepresenting a target frame. The system may use the unit cube's eightvertices to represent combination of zero or more subframe identifiers(e.g., OFF, S1, S2, S3, S1+S2, S1+S3, S2+S3, S1+S2+S3). The unit cubemay be divided into six tetrahedrons four of which may be used fordetermining the barycentric coordinate system. For a target grayscalevalue (e.g., an average grayscale value of a tile region of thedithering mask size), the system may first determine which of thetetrahedrons (e.g., one of the four tetrahedrons) that the grayscalevalue falls in based on the threshold ranges associated with thetetrahedrons. Then, the system may determine the barycentric weights ofthe target grayscale value with respect to the vertices of thetetrahedron. After that, the system may determine four non-overlappingdot sets of the dither mask (e.g., a blue-noise dithering mask)corresponding to the four barycentric weight values. Then, the systemmay determine the dot that are to be turned on in each of the threesubframes based on the four non-overlapping dot sets of the ditheringmask and a set of rules for assigning dots to the subframes. As aresult, the system may generate three subframes satisfying aspatial-stacking property as determined by the dithering mask and therules for assigning dots to the subframes.

In particular embodiments, the system may first receive a target pixelvalue p which could be an average pixel value of a target region of atarget image. The system may first determine which range the targetpixel value p falls within among the four value ranges of 0≤p<⅓, ⅓≤p<½,½≤p<⅔, and ⅔≤p≤1. Then, the system may determine an associatedbarycentric coordinate system corresponding to one of the fourtetrahedrons based on the value range that the target pixel value fallswithin. Then, the system may determine the barycentric weights for thetarget pixel value based on the associated barycentric coordinate systemcorresponding to the associated tetrahedron. In particular embodiments,for the four pixel value ranges of 0≤p<⅓, ⅓≤p<½, ½≤p<⅔, and ⅔≤p≤1, thesystem may determine the barycentric weights for the target pixel valuep based on weight vectors of [1−3p, p, p, p], [1−2p, p, 1−2p, 3p−1],[2p−1, 2p−1, 2−3p, 1−p], and [1−p, 1−p, 1−p, 3p−2], respectively. Eachcomponent of the weight vectors may correspond to a barycentric weight.The four pixel value ranges of 0≤p<⅓, ⅓≤p<½, ½≤p<⅔, and ⅔≤p≤1 may beassociated with four tetrahedrons which are associated with subframecombination identifiers of [OFF, S1, S2, S3], [S1, S2, S3, S1+3],[S1+S3, S2+S3, S2, S1+S2], and [S1+S3, S2+S3, S1+S2, S1+S2+S3],respectively. The system may determine four non-overlapping dot sets ofthe dithering mask based on the barycentric weight values of the targetpixel value and assign the dots of the non-overlapping dot sets todifferent subframes based on the corresponding subframe combinationidentifiers, as will be described later in this disclosure.

In particular embodiments, when the target pixel value p falls withinthe value range of 0≤p<⅓, the system may determine that the target pixelvalue p falls within the first tetrahedron of the four tetrahedrons ofthe unit cube. The system may determine the barycentric weights based ona weight vector of [1−3p, p, p, p] associated with the first tetrahedronof the unit cube. Each component of the weight vector may be used fordetermining a corresponding barycentric weight. The system may use asubframe identifier vector of [OFF, S1, S2, S3], which is associatedwith the first tetrahedron, for determining the combinations ofsubframes for the pixel value range of 0≤p<⅓. Each component of thesubframe identifier vector may correspond to a combination of zero ormore subframe identifiers. Then, the system may determine fournon-overlapping dot sets of the dithering mask based on the fourbarycentric weights of 1−3p, p, p, and p. For example, the system maydetermine a first dot set A1 including dots in the dithering mask havingthreshold values below 1−3p, a second dot set B1 including dots in thedithering mask having threshold values in the range of [1−3p, (1−3p)+p],a third dot set C1 including dots in the dithering mask having thresholdvalues in the range of [(1−3p)+p, (1−3p)+p+p], and a fourth dot set D1including dots in the dithering mask having threshold values on therange of [(1−3p)+p+p, 1]. Each dot set of the four non-overlapping dotsets may include a percentage of dots of the total dots of the ditheringmask corresponding to a barycentric weight value of [1−3p, p, p, p]. Inparticular embodiments, the system may generate three subframes based onthe four non-overlapping dot sets by: (1) excluding the dots the firstdot set A1 from any of the three subframes (i.e., the dots of the firstdot set A1 are not turned on in any subframes and remain dark); (2)including (i.e., turning on) the dots in the second dot set B1 in thefirst subframe S1; (3) including (i.e., turning on) the dost in thethird dot set C1 in the second subframe S2; and (4) including (i.e.,turning on) the dots in the fourth dot set D1 in the third subframe S3.As a result, the three subframes may each include a unique dot set whichdoes not share any dots with other subframes, and therefore satisfy thespatial stacking property.

As an example not by way limitation, for a target pixel value p=0.1 froma target image, the system may select the barycentric coordinate systemcorresponding to the first tetrahedron, which is associated withsubframe identifiers of [OFF, S1, S2, S3], based on a determination thatthe pixel value 0.1 falls within the first tetrahedron. The system maydetermine, for the target pixel value p=0.1, the barycentric weightvalues of [0.7, 0.1, 0.1, 0.1] based on the weight vector of [1−3p, p,p, p] associated with the first tetrahedron. Then, the system maydetermine, using the dithering mask having a blue-noise property, fournon-overlapping dot sets having 70%, 10%, 10%, and 10% of the total dotsof the dithering mask, respectively. The threshold values associatedwith the dots in the dithering mask may be normalized into a range of[0, 1]. The first dot set may include the dots of the dithering maskhaving threshold values below 0.7. The second dot set may include thedots of the dithering mask having threshold values in the range of [0.7,0.8]. The third dot set may include the dots of the dithering maskhaving threshold values in the range of [0.8, 0.9]. The fourth dot setmay include the dots of the dithering mask having threshold values inthe range of [0.9, 1]. For generating three subframes to represent thetarget image, the system may exclude the dots of the first dot set,which includes the dots of the dithering mask having threshold valuesbelow 0.7, from any subframes. In order words, the dots of the first dotset may be turned off and kept dark. The system may include the dots ofthe second dot set, which includes the dots of the dithering mask havingthreshold values in the range of [0.7, 0.8], in the first subframe S1.In other words, the dots of the second dot set may be turned on in thefirst subframe S1. The system may include the dots of the third dot set,which includes the dots in the dithering mask having threshold values inthe range of [0.8, 0.9], in the second subframe S2. In other words, thedots of the third dot set may be turned on in the second subframe S2.Then, the system may include the dots of the fourth dot set, whichinclude the dots in the dithering mask having threshold values in therange of [0.9, 1], in the second subframe S3. In other words, the dotsof the fourth dot set may be turned on in the second subframe S3. As aresult, the system may generate three subframes satisfying the spatialstacking property as determined by the non-overlapping dot sets and thedithering mask. The first, second, and third subframes may each include10% dots of the total dots in the dithering mask. The dot densities(percentage of dots with respect to the total dots in the ditheringmask) for representing the target pixel value in the three subframes mayhave a temporal average value of 0.1 matching the target pixel value0.1.

In particular embodiments, when the target pixel value p falls withinthe value range of ⅓≤p<½, the system may determine that the target pixelvalue p falls within the second tetrahedron of the four tetrahedrons ofthe unit cube. The system may determine the barycentric weights based ona weight vector of [1−2p, p, 1−2p, 3p−1] which is associated with thesecond tetrahedron of the unit cube. Each component of the weight vectormay be used to determine a corresponding barycentric weight. The systemmay use a subframe identifier vector of [S1, S2, S3, S1+S3], which isassociated with the second tetrahedron, for determining the combinationsof subframes for the pixel value range of ⅓≤p<½. Each component of thesubframe identifier vector may correspond to a combination of zero ormore subframe identifiers. Then, the system may determine fournon-overlapping dot sets of the dithering mask based on the fourbarycentric weights of 1−2p, p, 1−2p, and 3p−1. For example, the systemmay determine a first dot set A2 including dots in the dithering maskhaving threshold values below 1−2p, a second dot set B2 including dotsin the dithering mask having threshold values in the range of [1−2p,(1−2p)+p], a third dot set C1 including dots in the dithering maskhaving threshold values in the range of [(1-2p)+p, (1−2p)+p+(1−2p)], anda fourth dot set D1 including dots in the dithering mask havingthreshold values on the range of [(1−2p)+p+(1−2p), 1]. Each dot set ofthe four non-overlapping dot sets may include a percentage of dots ofthe total dots in the mask corresponding to a barycentric weight valueof [1−2p, p, 1−2p, 3p−1]. In particular embodiments, the system maygenerate the three subframes based on the four non-overlapping dot setsby: (1) including (i.e., turning on) the dots the first dot set A2 inthe first subframe S1; (2) including (i.e., turning on) the dots in thesecond dot set B2 in the second subframe S2; (3) including (i.e.,turning on) the dost in the third dot set C2 in the third subframe S3;and (4) including (i.e., turning on) the dots in the fourth dot set D2in the first and third subframe S1+S3. As a result, the three subframesmay include dot sets satisfying the spatial stacking property asdetermined by the dithering mask.

As an example not by way limitation, for a target pixel value p=0.4 froma target image, the system may select the barycentric coordinate systemcorresponding to the second tetrahedron, which is associated withsubframe identifiers of [S1, S2, S3, S1+S3], based on a determinationthat the pixel value 0.4 falls within the second tetrahedron. The systemmay determine, for the target pixel value p=0.4, the barycentric weightvalues of [0.2, 0.4, 0.2, 0.2] based on the weight vector of [1−2p, p,1−2p, 3p−1] associated with the second tetrahedron. Then, the system maydetermine, using the dithering mask having a blue-noise property, fournon-overlapping dot sets having 20%, 40%, 20%, and 20% of the total dotsof the dithering mask, respectively. The threshold values associatedwith the dots in the dithering mask may be normalized into a range of[0, 1]. The first dot set may include the dots of the dithering maskhaving threshold values below 0.2. The second dot set may include thedots of the dithering mask having threshold values in the range of [0.2,0.6]. The third dot set may include the dots of the dithering maskhaving threshold values in the range of [0.6, 0.8]. The fourth dot setmay include the dots of the dithering mask having threshold values inthe range of [0.8, 1]. For generating three subframes to represent thetarget image, the system may include the dots of the first dot set,which includes the dots of the dithering mask having threshold valuesbelow 0.2, in the first subframe S1. In order words, the dots of thefirst dot set may be turned on in the first subframe S1. The system mayinclude the dots of the second dot set, which includes the dots of thedithering mask having threshold values in the range of [0.2, 0.6], inthe second subframe S2. In other words, the dots of the second dot setmay be turned on in the second subframe S2. The system may include thedots of the third dot set, which includes the dots in the dithering maskhaving threshold values in the range of [0.6, 0.8], in the thirdsubframe S3. In other words, the dots of the third dot set may be turnedon in the third subframe S3. Then, the system may include the dots ofthe fourth dot set, which includes the dots in the dithering mask havingthreshold values in the range of [0.8, 1], in the first and thirdsubframe S1+S3. In other words, the dots of the fourth dot set may beturned on in the first and third subframes S1+S3. As a result, thesystem may generate three subframes satisfying the spatial stackingproperty as determined by the dithering mask. The first, second, andthird subframe may each include 40% dots of the total dots of thedithering mask for representing the target pixel value. The temporalaverage of the dot densities in the three subframes (percentage of dotswith respect to the total dots in the dithering mask) may equal to 0.4matching the target pixel value 0.4.

In particular embodiments, when the target pixel value p falls withinthe value range of ½≤p<⅔, the system may determine that the target pixelvalue p falls within the third tetrahedron of the four tetrahedrons ofthe unit cube. The system may determine the barycentric weights based ona weight vector of [2p−1, 2p−1, 2−3p, 1] which is associated with thethird tetrahedron of the unit cube. Each component of the weight vectormay be used to determine a corresponding barycentric weight. The systemmay use a subframe identifier vector of [S1+S3, S2+S3, S2, S1+S2], whichis associated with the third tetrahedron, for determining thecombinations of subframes for the pixel value range of ½≤p<⅔. Eachcomponent of the subframe identifier vector may correspond to acombination of zero or more subframe identifiers. Then, the system maydetermine four non-overlapping dot sets of the dithering mask based onthe four barycentric weights of 2p−1, 2p−1, 2−3p, and 1−p. For example,the system may determine a first dot set A3 including dots in thedithering mask having threshold values below 2p−1, a second dot set B3including dots in the dithering mask having threshold values in therange of [2p−1, (2p−1)+(2p−1)], a third dot set C3 including dots in thedithering mask having threshold values in the range of [(2p−1)+(2p−1),(2p−1)+(2p−1)+(2−3p)], and a fourth dot set D3 including dots in thedithering mask having threshold values on the range of[(2p−1)+(2p−1)+(2−3p), 1]. Each dot set of the four non-overlapping dotsets may include a percentage of dots of the total dots in the maskcorresponding to a barycentric weight value of [2p−1, 2p−1, 2−3p, 1−p].In particular embodiments, the system may generate the three subframesbased on the four non-overlapping dot sets by: (1) including (i.e.,turning on) the dots the first dot set A3 in the first and thirdsubframes S1+S3; (2) including (i.e., turning on) the dots in the seconddot set B3 in the second and third subframes S2+S3; (3) including (i.e.,turning on) the dost in the third dot set C3 in the second subframe S2;and (4) including (i.e., turning on) the dots in the fourth dot set D3in the first and second subframe S1+S2. As a result, the three subframesmay include dot sets satisfying the spatial stacking property asdetermined by the dithering mask.

As an example not by way limitation, for a target pixel value p=0.6 froma target image, the system may select the barycentric coordinate systemcorresponding to the third tetrahedron, which is associated withsubframe identifiers of [S1+S3, S2+S3, S2, S1+S2], based on adetermination that the pixel value 0.6 falls within the thirdtetrahedron. The system may determine, for the target pixel value p=0.6,the barycentric weight values of [0.2, 0.2, 0.2, 0.4] based on theweight vector of [2p−1, 2p−1, 2−3p, 1−p] associated with the thirdtetrahedron. Then, the system may determine, using the dithering maskhaving a blue-noise property, four non-overlapping dot sets having 20%,20%, 20%, and 40% of the total dots of the dithering mask, respectively.The threshold values associated with the dots in the dithering mask maybe normalized into a range of [0, 1]. The first dot set may include thedots of the dithering mask having threshold values below 0.2. The seconddot set may include the dots of the dithering mask having thresholdvalues in the range of [0.2, 0.4]. The third dot set may include thedots of the dithering mask having threshold values in the range of [0.4,0.6]. The fourth dot set may include the dots of the dithering maskhaving threshold values in the range of [0.6, 1]. For generating thethree subframes to represent the target image, the system may includethe dots of the first dot set, which includes the dots of the ditheringmask having threshold values below 0.2, in the first and third subframesS1+S3. In order words, the dots of the first dot set may be turned on inthe first and third subframes S1+S3. The system may include the dots ofthe second dot set, which includes the dots of the dithering mask havingthreshold values in the range of [0.2, 0.4], in the second and thirdsubframes S2+S3. In other words, the dots of the second dot set may beturned on in the second and third subframes S2+S3. The system mayinclude the dots of the third dot set, which includes the dots in thedithering mask having threshold values in the range of [0.4, 0.6], inthe second subframe S2. In other words, the dots of the third dot setmay be turned on in the second subframe S2. Then, the system may includethe dots of the fourth dot set, which includes the dots in the ditheringmask having threshold values in the range of [0.6, 1], in the first andsecond subframe S1+S2. In other words, the dots of the fourth dot setmay be turned on in the first and second subframes S1+S2. As a result,the system may generate three subframes satisfying the spatial stackingproperty as determined by the dithering mask. The first, second, andthird subframe may include 60%, 80%, and 40% dots of the total dots ofthe dithering mask, respectively, for representing the target pixelvalue. The dot densities (percentage of dots with respect to the totaldots in the dithering mask) in three subframes may have a temporalaverage equal to 0.6 matching the target pixel value 0.6.

In particular embodiments, when the target pixel value p falls withinthe value range of ⅔≤p<1, the system may determine that the target pixelvalue p falls within the fourth tetrahedron of the four tetrahedrons ofthe unit cube. The system may determine the barycentric weights based ona weight vector of [1−p, 1−p, 1−p, 3p−2] which is associated with thefourth tetrahedron. Each component of the weight vector may be used todetermine a barycentric weight. The system may use a subframe identifiervector of [S1+S3, S2+S3, S1+S2, S1+S2+S3], which is associated with thefourth tetrahedron, for determining the combinations of subframes forthe pixel value range of ⅔≤p<1. Each component of the subframeidentifier vector may correspond to a combination of zero or moresubframe identifiers. Then, the system may determine fournon-overlapping dot sets of the dithering mask based on the fourbarycentric weights of 1−p, 1−p, 1−p, and 3p−2. For example, the systemmay determine a first dot set A4 including dots in the dithering maskhaving threshold values below 1−p, a second dot set B4 including dots inthe dithering mask having threshold values in the range of [1−p,(1−p)+(1−p)], a third dot set C4 including dots in the dithering maskhaving threshold values in the range of [(1−p)+(1−p),(1−p)+(1−p)+(1−p)], and a fourth dot set D4 including dots in thedithering mask having threshold values on the range of[(1−p)+(1−p)+(1−p), 1]. Each dot set of the four non-overlapping dotsets may include a percentage of dots of the total dots in the maskcorresponding to a barycentric weight value of [1−p, 1−p, 1−p, 3p−2p].In particular embodiments, the system may generate three subframes basedon the four non-overlapping dot sets by: (1) including (i.e., turningon) the dots the first dot set A4 in the first and third subframesS1+S3; (2) including (i.e., turning on) the dots in the second dot setB4 in the second and third subframes S2+S3; (3) including (i.e., turningon) the dost in the third dot set C4 in the first and second subframesS1+S2; and (4) including (i.e., turning on) the dots in the fourth dotset D4 in the first, second, and third subframes S1+S2+S3. As a result,the three subframes may include dot sets satisfying the spatial stackingproperty as determined by the dithering mask.

As an example not by way limitation, for a target pixel value p=0.7 froma target image, the system may select the barycentric coordinate systemcorresponding to the fourth tetrahedron, which is associated withsubframe identifiers of [S1+S3, S2+S3, S1+S2, S1+S2+S3], based on adetermination that the pixel value 0.7 falls within the fourthtetrahedron. The system may determine, for the target pixel value p=0.7,the barycentric weight values of [0.3, 0.3, 0.3, 0.1] based on theweight vector of [1−p, 1−p, 1−p, 3p−2] associated with the fourthtetrahedron. Then, the system may determine, using the dithering maskhaving a blue-noise property, four non-overlapping dot sets having 30%,30%, 30%, and 10% of the total dots of the dithering mask, respectively.The threshold values associated with the dots in the dithering mask maybe normalized into a range of [0, 1]. The first dot set may include thedots of the dithering mask having threshold values below 0.3. The seconddot set may include the dots of the dithering mask having thresholdvalues in the range of [0.3, 0.6]. The third dot set may include thedots of the dithering mask having threshold values in the range of [0.6,0.9]. The fourth dot set may include the dots of the dithering maskhaving threshold values in the range of [0.9, 1]. For generating thethree subframes to represent the target image, the system may includethe dots of the first dot set, which includes the dots of the ditheringmask having threshold values below 0.3, in the first and third subframesS1+S3. In order words, the dots of the first dot set may be turned on inthe first and third subframes S1+S3. The system may include the dots ofthe second dot set, which includes the dots of the dithering mask havingthreshold values in the range of [0.3, 0.6], in the second and thirdsubframes S2+S3. In other words, the dots of the second dot set may beturned on in the second and third subframes S2+S3. The system mayinclude the dots of the third dot set, which includes the dots in thedithering mask having threshold values in the range of [0.6, 0.9], inthe first and second subframes S1+S2. In other words, the dots of thethird dot set may be turned on in the first and second subframe S1+S2.Then, the system may include the dots of the fourth dot set, whichincludes the dots in the dithering mask having threshold values in therange of [0.9, 1], in the first, second, and third subframe S1+S2+S3. Inother words, the dots of the fourth dot set may be turned on in thefirst, second, and third subframes S1+S2+S3. As a result, the system maygenerate three subframes satisfying the spatial stacking property asdetermined by the dithering mask. The first, second, and third subframemay each include 70% dots of the total dots of the dithering mask forrepresenting the target pixel value. The temporal average of the dotdensity (percentage of dots with respect to the total dots in thedithering mask) of the three subframes may equal to 0.7 matching thetarget pixel value 0.7.

In particular embodiments, for an image having a larger size than thedithering mask, the dithering mask may be replicated to cover the image.To determine which subframe(s) should include a given dot of thedithering mask, the system may first determine a threshold value Qassociated with that dot based on a replicated dithering mask using thefollowing equation:Q=mask(mod(x,M)+1,mod(y,M)+1)  (1)where, x and y are position coordinates of an associated pixel of thedot, M×M is the size of the dithering mask, mod is the module operator.Since the barycentric weights of a target pixel value with respect to abarycentric coordinate system may sum to unity and the threshold valuesof the blue noise mask may normalized to a range of [0, 1], the systemuse the mask to choose the tetrahedron vertex based on the cumulativesum of the barycentric weights. In particular embodiments, thetetrahedron vertex v_(k) may be chosen when the sum of the first kbarycentric weights exceeds the threshold value Q associated with thatdot as represented by the following equation:

$\begin{matrix}{v = {{v_{k}\mspace{14mu}{for}{\mspace{11mu}\;}{which}\mspace{14mu}{\sum\limits_{i}^{k}\; w_{i}}} > Q}} & (1)\end{matrix}$where, v_(k) is the selected tetrahedron vertex, w_(i) is the i-thbarycentric weight, Q is the threshold hold value associated with thatdot. The system may compare the threshold value Q to the cumulative sumof the barycentric weights of the target grayscale value with respect tothe associated barycentric coordinate system. The system may select thetetrahedron vertex v_(k) when the sum of the first k barycentric weightsexceeds the threshold value Q. The tetrahedron vertex v_(k) may beassociated with zero or more subframe identifiers. The system may assignthis dot to the zero or more subframes corresponding to the selectedtetrahedron vertex v_(k).

As an example and not by way of limitation, for a target pixel value of0.1, the system may determine barycentric weights of [0.7, 0.1, 0.1,0.1] with respect to a barycentric coordinate system corresponding to atetrahedron that the target pixel value falls within. The four verticesof the tetrahedron may be associated with subframe identifiers of OFF,S1, S2, and S3, respectively. Given a threshold value Q in a range of0≤p<0.7, the system may select the first vertex v₁ based on adetermination that the first barycentric weight 0.7 is greater than thethreshold value Q. Since the subframe identifier corresponding to thefirst vertex v₁ is OFF, the system may not include the corresponding dotof this pixel in any subframes. Given a threshold value Q in a range of0.7≤p<0.8, the system may select the second vertex v₂ based on adetermination that the sum of the first barycentric weight 0.7 and thesecond barycentric weight 0.1 is greater than the threshold value Q.Since the subframe identifier corresponding to the second vertex v₁ isS1, the system may include the corresponding dot in the first subframeS1. Given a threshold value Q in a range of 0.8≤p<0.9, the system mayselect the third vertex v₃ based on a determination that the sum of thefirst, second, and third barycentric weight (0.7+0.1+0.1=0.9) is greaterthan the threshold value Q. Since the subframe identifier correspondingto the third vertex v₃ is S2, the system may include the correspondingdot in the second subframe S2. Given a threshold value Q in a range of0.9≤p<1, the system may select the fourth vertex v₄ based on adetermination that the sum of the first, second, third, and thirdbarycentric weights (0.7+0.1+0.1+0.1=1) is greater than the thresholdvalue Q. Since the subframe identifier corresponding to the fourthvertex v₄ is S3, the system may include the corresponding dot of thispixel in the third subframe S3.

FIG. 7 illustrates an example method 700 for generating a number ofsubframes based on a barycentric coordinate system and a dithering maskfor representing a target frame. The method may begin at step 710, wherea computing system may determine that a target grayscale value p for aframe falls within one of a number of predetermined grayscale ranges. Atstep 720, the system may compute, based on the target grayscale value p,barycentric weights for a predetermined barycentric coordinate systemassociated with one of the predetermined grayscale ranges. Thebarycentric coordinate system may be associated with vertices that eachrepresents a combination of zero or more subframe identifiers selectedfrom a number of subframe identifiers. At step 730, the system mayselect, using the barycentric weights and threshold values associatedwith respective dots in a dithering mask, a set of non-overlapping dotpatterns from the dithering mask corresponding to the vertices of thebarycentric coordinate system. The dots in the dithering mask maysatisfy a spatial stacking constraint according to the threshold valuesassociated with the dots. At step 740, the system may generate a numberof subframes corresponding to the subframe identifiers to represent theframe. The subframes may be generated based on the set ofnon-overlapping dot patterns and the subframe combination represented byeach of the vertices.

In particular embodiments, the barycentric coordinate system maycorrespond to a tetrahedron of a unit cube. The vertices of thebarycentric coordinate system may correspond to four vertices of thetetrahedron for representing four combinations of subframe identifiers.Each combination of subframe identifiers may include zero or moresubframe identifiers. In particular embodiments, the set ofnon-overlapping dot patterns may be selected based on a comparisonbetween accumulative barycentric weight values and correspondingthreshold values of the dithering mask. In particular embodiments, eachdot of the dithering mask may correspond to a threshold value. Thethreshold value associated with a dot may correspond to a smallestthreshold value associated with a dot pattern including that dot. Thedithering mask may have a blue-noise property and may include a numberof dot patterns each satisfying the spatial stacking constraint byincluding all dot patterns associated with smaller threshold values.

In particular embodiments, the subframes may include three subframes.When the grayscale value p is in a range of 0≤p<⅓, the system maydetermine the barycentric weights using a weight vector of [1−3p, p, p,p]. The corresponding subframe identifiers may include four subframeidentifiers corresponding to OFF, a first subframe S1, a second subframeS2, and a third subframe S3, respectively. In particular embodiments,the set of non-overlapping dot patterns may include a firstnon-overlapping dot pattern comprising dots in the dithering mask havingthreshold values below a first threshold of 1−3p, a secondnon-overlapping dot pattern comprising dots in the dithering mask havingthreshold values in a range of [1−3p, 1−2p], a third non-overlapping dotpattern comprising dots in the dithering mask having threshold values ina range of [1−2p, 1−p], and a fourth non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [1−p, 1]. In particular embodiments, the first, second and thirdsubframes may be generated by: excluding dots in the firstnon-overlapping dot pattern from the first, second and third subframes,including dots in the second non-overlapping dot pattern to the firstsubframe S1, including dots in the third non-overlapping dot pattern tothe second subframe S2, and including dots in the fourth non-overlappingdot pattern to the third subframe S3.

In particular embodiments, when the grayscale value is in a range of⅓≤p<½, the system may determine the barycentric weights using a weightvector of [1−2p, p, 1−2p, 3p−1]. The corresponding subframe identifiersmay include four subframe identifiers corresponding to a first subframeS1, a second subframe S2, a third subframe S3, and a combination of thefirst subframe S1 and the third subframe S3, respectively. In particularembodiments, the set of non-overlapping dot patterns may include a firstnon-overlapping dot pattern comprising dots in the dithering mask havingthreshold values below a first threshold of 1−2p, a secondnon-overlapping dot pattern comprising dots in the dithering mask havingthreshold values in a range of [1−2p, 1−p], a third non-overlapping dotpattern comprising dots in the dithering mask having threshold values ina range of [1−p, 2−3p], and a fourth non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [2−3p, 1]. In particular embodiments, the first, second and thirdsubframes may be generated by: including dots in the firstnon-overlapping dot pattern to the first subframe S1, including dots inthe second non-overlapping dot pattern to the second subframe S2,including dots in the third non-overlapping dot pattern to the thirdsubframe S3, and including dots in the fourth non-overlapping dotpattern to the first subframe S1 and the third subframe S3.

In particular embodiments, when the grayscale value p is in a range of½≤p<⅔, the system may determine the barycentric weights using a weightvector of [2p−1, 2p−1, 2−3p, 1−p]. The corresponding subframeidentifiers may include four subframe identifiers corresponding to afirst combination of a first subframe S1 and a third subframe S3, asecond combination of a second subframe S2 and the third subframe S3,the second subframe S2, and a third combination of the first subframe S1and the second subframe S2, respectively. In particular embodiments, theset of non-overlapping dot patterns may include a first non-overlappingdot pattern comprising dots on the dithering mask having thresholdvalues below a first threshold of 2p−1, a second non-overlapping dotpattern comprising dots in the dithering mask having threshold values ina range [2p−1, 4p−2], a third non-overlapping dot pattern comprisingdots in the dithering mask having threshold values in a region of [4p−2,p], and a fourth non-overlapping dot pattern comprising dots in thedithering mask having threshold values in a range of [p, 1]. Inparticular embodiments, the first, second and third subframes aregenerated by: including dots in the first non-overlapping dot pattern tothe first subframe S1 and the third subframe S3, including dots in thesecond non-overlapping dot pattern to the second subframe S2 and thethird subframe S3, including dots in the third non-overlapping dotpattern to the second subframe S2, and including dots in the fourthnon-overlapping dot pattern to the first subframe S1 and the secondsubframe S2.

In particular embodiments, when the grayscale value p is in a range of⅔≤p<1, the system may determine barycentric weights using a weightvector of [1−p, 1−p, 1−p, 3p−2]. The corresponding subframe identifiersmay include four subframe identifiers corresponding to a firstcombination of a first subframe S1 and a third subframe S3, a secondcombination of a second subframe S2 and the third subframe S3, a thirdcombination of the first subframe S1 and the second subframe S2, and athird combination of the first subframe S1, the second subframe S2, andthe third subframe S3, respectively. In particular embodiments, the setof non-overlapping dot patterns may include a first non-overlapping dotpattern comprising dots in the dithering mask having threshold valuesbelow a first threshold of 1−p, a second non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [1−p, 2−2p], a third non-overlapping dot pattern comprising dots inthe dithering mask having threshold values in a range of [2−2p, 3−3p],and a fourth non-overlapping dot pattern comprising dots in thedithering mask having threshold values in a range of [3−3p, 1]. Inparticular embodiments, the first, second and third subframes may begenerated by: including dots in the first non-overlapping dot pattern tothe first subframe S1 and the third subframe S3, including dots in thesecond non-overlapping dot pattern to the second subframe S2 and thethird subframe S3, including dots in the third non-overlapping dotpattern to the first subframe S1 and the second subframe S2, andincluding dots in the fourth non-overlapping dot pattern to the firstsubframe S1, the second subframe S2, and the third subframe S3. Inparticular embodiments, the target grayscale value may be an averagegrayscale value of a target region of a target image. The target imagemay have a larger size than the dithering mask. The dithering mask maybe replicated to cover the target image.

Particular embodiments may repeat one or more steps of the method ofFIG. 7, where appropriate. Although this disclosure describes andillustrates particular steps of the method of FIG. 7 as occurring in aparticular order, this disclosure contemplates any suitable steps of themethod of FIG. 7 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates an example method forgenerating a number of subframes based on a barycentric coordinatesystem and a dithering mask for representing a target frame includingthe particular steps of the method of FIG. 7, this disclosurecontemplates any suitable method for generating a number of subframesbased on a barycentric coordinate system and a dithering mask forrepresenting a target frame including any suitable steps, which mayinclude all, some, or none of the steps of the method of FIG. 7, whereappropriate. Furthermore, although this disclosure describes andillustrates particular components, devices, or systems carrying outparticular steps of the method of FIG. 7, this disclosure contemplatesany suitable combination of any suitable components, devices, or systemscarrying out any suitable steps of the method of FIG. 7.

FIG. 8 illustrates an example computer system 800. In particularembodiments, one or more computer systems 800 perform one or more stepsof one or more methods described or illustrated herein. In particularembodiments, one or more computer systems 800 provide functionalitydescribed or illustrated herein. In particular embodiments, softwarerunning on one or more computer systems 800 performs one or more stepsof one or more methods described or illustrated herein or providesfunctionality described or illustrated herein. Particular embodimentsinclude one or more portions of one or more computer systems 800.Herein, reference to a computer system may encompass a computing device,and vice versa, where appropriate. Moreover, reference to a computersystem may encompass one or more computer systems, where appropriate.

This disclosure contemplates any suitable number of computer systems800. This disclosure contemplates computer system 800 taking anysuitable physical form. As example and not by way of limitation,computer system 800 may be an embedded computer system, a system-on-chip(SOC), a single-board computer system (SBC) (such as, for example, acomputer-on-module (COM) or system-on-module (SOM)), a desktop computersystem, a laptop or notebook computer system, an interactive kiosk, amainframe, a mesh of computer systems, a mobile telephone, a personaldigital assistant (PDA), a server, a tablet computer system, anaugmented/virtual reality device, or a combination of two or more ofthese. Where appropriate, computer system 800 may include one or morecomputer systems 800; be unitary or distributed; span multiplelocations; span multiple machines; span multiple data centers; or residein a cloud, which may include one or more cloud components in one ormore networks. Where appropriate, one or more computer systems 800 mayperform without substantial spatial or temporal limitation one or moresteps of one or more methods described or illustrated herein. As anexample and not by way of limitation, one or more computer systems 800may perform in real time or in batch mode one or more steps of one ormore methods described or illustrated herein. One or more computersystems 800 may perform at different times or at different locations oneor more steps of one or more methods described or illustrated herein,where appropriate.

In particular embodiments, computer system 800 includes a processor 802,memory 804, storage 806, an input/output (I/O) interface 808, acommunication interface 810, and a bus 812. Although this disclosuredescribes and illustrates a particular computer system having aparticular number of particular components in a particular arrangement,this disclosure contemplates any suitable computer system having anysuitable number of any suitable components in any suitable arrangement.

In particular embodiments, processor 802 includes hardware for executinginstructions, such as those making up a computer program. As an exampleand not by way of limitation, to execute instructions, processor 802 mayretrieve (or fetch) the instructions from an internal register, aninternal cache, memory 804, or storage 806; decode and execute them; andthen write one or more results to an internal register, an internalcache, memory 804, or storage 806. In particular embodiments, processor802 may include one or more internal caches for data, instructions, oraddresses. This disclosure contemplates processor 802 including anysuitable number of any suitable internal caches, where appropriate. Asan example and not by way of limitation, processor 802 may include oneor more instruction caches, one or more data caches, and one or moretranslation lookaside buffers (TLBs). Instructions in the instructioncaches may be copies of instructions in memory 804 or storage 806, andthe instruction caches may speed up retrieval of those instructions byprocessor 802. Data in the data caches may be copies of data in memory804 or storage 806 for instructions executing at processor 802 tooperate on; the results of previous instructions executed at processor802 for access by subsequent instructions executing at processor 802 orfor writing to memory 804 or storage 806; or other suitable data. Thedata caches may speed up read or write operations by processor 802. TheTLBs may speed up virtual-address translation for processor 802. Inparticular embodiments, processor 802 may include one or more internalregisters for data, instructions, or addresses. This disclosurecontemplates processor 802 including any suitable number of any suitableinternal registers, where appropriate. Where appropriate, processor 802may include one or more arithmetic logic units (ALUs); be a multi-coreprocessor; or include one or more processors 802. Although thisdisclosure describes and illustrates a particular processor, thisdisclosure contemplates any suitable processor.

In particular embodiments, memory 804 includes main memory for storinginstructions for processor 802 to execute or data for processor 802 tooperate on. As an example and not by way of limitation, computer system800 may load instructions from storage 806 or another source (such as,for example, another computer system 800) to memory 804. Processor 802may then load the instructions from memory 804 to an internal registeror internal cache. To execute the instructions, processor 802 mayretrieve the instructions from the internal register or internal cacheand decode them. During or after execution of the instructions,processor 802 may write one or more results (which may be intermediateor final results) to the internal register or internal cache. Processor802 may then write one or more of those results to memory 804. Inparticular embodiments, processor 802 executes only instructions in oneor more internal registers or internal caches or in memory 804 (asopposed to storage 806 or elsewhere) and operates only on data in one ormore internal registers or internal caches or in memory 804 (as opposedto storage 806 or elsewhere). One or more memory buses (which may eachinclude an address bus and a data bus) may couple processor 802 tomemory 804. Bus 812 may include one or more memory buses, as describedbelow. In particular embodiments, one or more memory management units(MMUs) reside between processor 802 and memory 804 and facilitateaccesses to memory 804 requested by processor 802. In particularembodiments, memory 804 includes random access memory (RAM). This RAMmay be volatile memory, where appropriate. Where appropriate, this RAMmay be dynamic RAM (DRAM) or static RAM (SRAM). Moreover, whereappropriate, this RAM may be single-ported or multi-ported RAM. Thisdisclosure contemplates any suitable RAM. Memory 804 may include one ormore memories 804, where appropriate. Although this disclosure describesand illustrates particular memory, this disclosure contemplates anysuitable memory.

In particular embodiments, storage 806 includes mass storage for data orinstructions. As an example and not by way of limitation, storage 806may include a hard disk drive (HDD), a floppy disk drive, flash memory,an optical disc, a magneto-optical disc, magnetic tape, or a UniversalSerial Bus (USB) drive or a combination of two or more of these. Storage806 may include removable or non-removable (or fixed) media, whereappropriate. Storage 806 may be internal or external to computer system800, where appropriate. In particular embodiments, storage 806 isnon-volatile, solid-state memory. In particular embodiments, storage 806includes read-only memory (ROM). Where appropriate, this ROM may bemask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM),electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM),or flash memory or a combination of two or more of these. Thisdisclosure contemplates mass storage 806 taking any suitable physicalform. Storage 806 may include one or more storage control unitsfacilitating communication between processor 802 and storage 806, whereappropriate. Where appropriate, storage 806 may include one or morestorages 806. Although this disclosure describes and illustratesparticular storage, this disclosure contemplates any suitable storage.

In particular embodiments, I/O interface 808 includes hardware,software, or both, providing one or more interfaces for communicationbetween computer system 800 and one or more I/O devices. Computer system800 may include one or more of these I/O devices, where appropriate. Oneor more of these I/O devices may enable communication between a personand computer system 800. As an example and not by way of limitation, anI/O device may include a keyboard, keypad, microphone, monitor, mouse,printer, scanner, speaker, still camera, stylus, tablet, touch screen,trackball, video camera, another suitable I/O device or a combination oftwo or more of these. An I/O device may include one or more sensors.This disclosure contemplates any suitable I/O devices and any suitableI/O interfaces 808 for them. Where appropriate, I/O interface 808 mayinclude one or more device or software drivers enabling processor 802 todrive one or more of these I/O devices. I/O interface 808 may includeone or more I/O interfaces 808, where appropriate. Although thisdisclosure describes and illustrates a particular I/O interface, thisdisclosure contemplates any suitable I/O interface.

In particular embodiments, communication interface 810 includeshardware, software, or both providing one or more interfaces forcommunication (such as, for example, packet-based communication) betweencomputer system 800 and one or more other computer systems 800 or one ormore networks. As an example and not by way of limitation, communicationinterface 810 may include a network interface controller (NIC) ornetwork adapter for communicating with an Ethernet or other wire-basednetwork or a wireless NIC (WNIC) or wireless adapter for communicatingwith a wireless network, such as a WI-FI network. This disclosurecontemplates any suitable network and any suitable communicationinterface 810 for it. As an example and not by way of limitation,computer system 800 may communicate with an ad hoc network, a personalarea network (PAN), a local area network (LAN), a wide area network(WAN), a metropolitan area network (MAN), or one or more portions of theInternet or a combination of two or more of these. One or more portionsof one or more of these networks may be wired or wireless. As anexample, computer system 800 may communicate with a wireless PAN (WPAN)(such as, for example, a BLUETOOTH WPAN), a WI-FI network, a WI-MAXnetwork, a cellular telephone network (such as, for example, a GlobalSystem for Mobile Communications (GSM) network), or other suitablewireless network or a combination of two or more of these. Computersystem 800 may include any suitable communication interface 810 for anyof these networks, where appropriate. Communication interface 810 mayinclude one or more communication interfaces 810, where appropriate.Although this disclosure describes and illustrates a particularcommunication interface, this disclosure contemplates any suitablecommunication interface.

In particular embodiments, bus 812 includes hardware, software, or bothcoupling components of computer system 800 to each other. As an exampleand not by way of limitation, bus 812 may include an AcceleratedGraphics Port (AGP) or other graphics bus, an Enhanced Industry StandardArchitecture (EISA) bus, a front-side bus (FSB), a HYPERTRANSPORT (HT)interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBANDinterconnect, a low-pin-count (LPC) bus, a memory bus, a Micro ChannelArchitecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, aPCI-Express (PCIe) bus, a serial advanced technology attachment (SATA)bus, a Video Electronics Standards Association local (VLB) bus, oranother suitable bus or a combination of two or more of these. Bus 812may include one or more buses 812, where appropriate. Although thisdisclosure describes and illustrates a particular bus, this disclosurecontemplates any suitable bus or interconnect.

Herein, a computer-readable non-transitory storage medium or media mayinclude one or more semiconductor-based or other integrated circuits(ICs) (such, as for example, field-programmable gate arrays (FPGAs) orapplication-specific ICs (ASICs)), hard disk drives (HDDs), hybrid harddrives (HHDs), optical discs, optical disc drives (ODDs),magneto-optical discs, magneto-optical drives, floppy diskettes, floppydisk drives (FDDs), magnetic tapes, solid-state drives (SSDs),RAM-drives, SECURE DIGITAL cards or drives, any other suitablecomputer-readable non-transitory storage media, or any suitablecombination of two or more of these, where appropriate. Acomputer-readable non-transitory storage medium may be volatile,non-volatile, or a combination of volatile and non-volatile, whereappropriate.

Herein, “or” is inclusive and not exclusive, unless expressly indicatedotherwise or indicated otherwise by context. Therefore, herein, “A or B”means “A, B, or both,” unless expressly indicated otherwise or indicatedotherwise by context. Moreover, “and” is both joint and several, unlessexpressly indicated otherwise or indicated otherwise by context.Therefore, herein, “A and B” means “A and B, jointly or severally,”unless expressly indicated otherwise or indicated otherwise by context.

The scope of this disclosure encompasses all changes, substitutions,variations, alterations, and modifications to the example embodimentsdescribed or illustrated herein that a person having ordinary skill inthe art would comprehend. The scope of this disclosure is not limited tothe example embodiments described or illustrated herein. Moreover,although this disclosure describes and illustrates respectiveembodiments herein as including particular components, elements,feature, functions, operations, or steps, any of these embodiments mayinclude any combination or permutation of any of the components,elements, features, functions, operations, or steps described orillustrated anywhere herein that a person having ordinary skill in theart would comprehend. Furthermore, reference in the appended claims toan apparatus or system or a component of an apparatus or system beingadapted to, arranged to, capable of, configured to, enabled to, operableto, or operative to perform a particular function encompasses thatapparatus, system, component, whether or not it or that particularfunction is activated, turned on, or unlocked, as long as thatapparatus, system, or component is so adapted, arranged, capable,configured, enabled, operable, or operative. Additionally, although thisdisclosure describes or illustrates particular embodiments as providingparticular advantages, particular embodiments may provide none, some, orall of these advantages.

What is claimed is:
 1. A method comprising, by a computing system:determining that a target grayscale value p for a frame falls within oneof a plurality of predetermined grayscale ranges; computing, based onthe target grayscale value p, barycentric weights for a predeterminedbarycentric coordinate system associated with the predeterminedgrayscale ranges, wherein the barycentric coordinate system isassociated with vertices that each represents a subframe combination ofzero or more subframe identifiers selected from a plurality of subframeidentifiers; selecting, using the barycentric weights and thresholdvalues associated with respective dots in a dithering mask, a set ofnon-overlapping dot patterns from the dithering mask corresponding tothe vertices of the barycentric coordinate system, wherein the dots inthe dithering mask satisfy a spatial stacking constraint according tothe threshold values associated with the dots; and generating aplurality of subframes corresponding to the plurality of subframeidentifiers to represent the frame, wherein the plurality of subframesare generated based on the set of non-overlapping dot patterns and thesubframe combination represented by each of the vertices.
 2. The methodof claim 1, wherein the barycentric coordinate system corresponds to atetrahedron of a unit cube, wherein the vertices of the barycentriccoordinate system correspond to four vertices of the tetrahedron forrepresenting four combination of subframe identifiers, and wherein eachcombination of subframe identifiers comprises zero or more subframeidentifiers.
 3. The method of claim 1, wherein the set ofnon-overlapping dot patterns are selected based on a comparison betweenaccumulative barycentric weight values and corresponding thresholdvalues of the dithering mask.
 4. The method of claim 1, wherein each dotof the dithering mask corresponds to a threshold value, and wherein thethreshold value corresponds to a smallest threshold value which has acorresponding dot pattern comprising that dot.
 5. The method of claim 4,wherein the dithering mask has a blue-noise property, wherein thedithering mask comprises a plurality of dot patterns each satisfying thespatial stacking constraint by comprising all dot patterns associatedwith smaller threshold values.
 6. The method of claim 1, wherein theplurality of subframes comprises three subframes, wherein the grayscalevalue p is in a range of 0≤p<⅓, wherein the barycentric weights aredetermined by a weight vector of [1−3p, p, p, p], and wherein theplurality of subframe identifiers comprises four subframe identifierscorresponding to OFF, a first subframe S1, a second subframe S2, and athird subframe S3, respectively.
 7. The method of claim 6, wherein theset of non-overlapping dot patterns comprise: a first non-overlappingdot pattern comprising dots in the dithering mask having thresholdvalues below a first threshold of 1−3p; a second non-overlapping dotpattern comprising dots in the dithering mask having threshold values ina range of [1−3p, 1−2p]; a third non-overlapping dot pattern comprisingdots in the dithering mask having threshold values in a range of [1−2p,1−p]; and a fourth non-overlapping dot pattern comprising dots in thedithering mask having threshold values in a range of [1−p, 1].
 8. Themethod of claim 7, wherein the first, second and third subframes aregenerated by: excluding dots in the first non-overlapping dot patternfrom the first, second and third subframes; including dots in the secondnon-overlapping dot pattern to the first subframe S1; including dots inthe third non-overlapping dot pattern to the second subframe S2; andincluding dots in the fourth non-overlapping dot pattern to the thirdsubframe S3.
 9. The method of claim 1, wherein the plurality ofsubframes comprises three subframes, wherein the grayscale value is in arange of ⅓≤p<½, wherein the barycentric weights are determined by aweight vector of [1−2p, p, 1−2p, 3p−1], and wherein the plurality ofsubframe identifiers comprises four subframe identifiers correspondingto a first subframe S1, a second subframe S2, a third subframe S3, and acombination of the first subframe S1 and the third subframe S3,respectively.
 10. The method of claim 9, wherein the set ofnon-overlapping dot patterns comprise: a first non-overlapping dotpattern comprising dots in the dithering mask having threshold valuesbelow a first threshold of 1−2p; a second non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [1−2p, 1−p]; a third non-overlapping dot pattern comprising dots inthe dithering mask having threshold values in a range of [1−p, 2−3p];and a fourth non-overlapping dot pattern comprising dots in thedithering mask having threshold values in a range of [2−3p, 1] in thedithering mask.
 11. The method of claim 10, wherein the first, second,and third subframes are generated by: including dots in the firstnon-overlapping dot pattern to the first subframe S1; including dots inthe second non-overlapping dot pattern to the second subframe S2;including dots in the third non-overlapping dot pattern to the thirdsubframe S3; and including dots in the fourth non-overlapping dotpattern to the first subframe S1 and the third subframe S3.
 12. Themethod of claim 1, wherein the plurality of subframes comprises threesubframes, wherein the grayscale value p is in a range of ½≤p<⅔, thebarycentric weights are determined by a weight vector of [2p−1, 2p−1,2−3p, 1−p], and wherein the plurality of subframe identifiers comprisesfour subframe identifiers corresponding to a first combination of afirst subframe S1 and a third subframe S3, a second combination of asecond subframe S2 and the third subframe S3, the second subframe S2,and a third combination of the first subframe S1 and the second subframeS2, respectively.
 13. The method of claim 12, wherein the set ofnon-overlapping dot patterns comprise: a first non-overlapping dotpattern comprising dots on the dithering mask having threshold valuesbelow a first threshold of 2p−1; a second non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [2p−1, 4p−2]; a third non-overlapping dot pattern comprising dots inthe dithering mask having threshold values in a range of [4p−2, p]; anda fourth non-overlapping dot pattern comprising dots in the ditheringmask having threshold values in a range of [p, 1].
 14. The method ofclaim 13, wherein the first, second and third subframes are generatedby: including dots in the first non-overlapping dot pattern to the firstsubframe S1 and the third subframe S3; including dots in the secondnon-overlapping dot pattern to the second subframe S2 and the thirdsubframe S3; including dots in the third non-overlapping dot pattern tothe second subframe S2; and including dots in the fourth non-overlappingdot pattern to the first subframe S1 and the second subframe S2.
 15. Themethod of claim 1, wherein the plurality of subframes comprises threesubframes, wherein the grayscale value p is in a range of ⅔≤p<1, whereinbarycentric weights are determined by a weight vector of [1−p, 1−p, 1−p,3p−2], and wherein plurality of subframe identifiers comprises foursubframe identifiers corresponding to a first combination of a firstsubframe S1 and a third subframe S3, a second combination of a secondsubframe S2 and the third subframe S3, a third combination of the firstsubframe S1 and the second subframe S2, and a third combination of thefirst subframe S1, the second subframe S2, and the third subframe S3,respectively.
 16. The method of claim 15, wherein the set ofnon-overlapping dot patterns comprise: a first non-overlapping dotpattern comprising dots in the dithering mask having threshold valuesbelow a first threshold of 1−p; a second non-overlapping dot patterncomprising dots in the dithering mask having threshold values in a rangeof [1−p, 2−2p]; a third non-overlapping dot pattern comprising dots inthe dithering mask having threshold values in a range of [2−2p, 3−3p];and a fourth non-overlapping dot pattern comprising dots in thedithering mask having threshold values in a range of [3−3p, 1].
 17. Themethod of claim 16, wherein the first, second and third subframes aredetermined by: including dots in the first non-overlapping dot patternto the first subframe S1 and the third subframe S3; including dots inthe second non-overlapping dot pattern to the second subframe S2 and thethird subframe S3; including dots in the third non-overlapping dotpattern to the first subframe S1 and the second subframe S2; andincluding dots in the fourth non-overlapping dot pattern to the firstsubframe S1, the second subframe S2, and the third subframe S3.
 18. Themethod of claim 1, wherein the target grayscale value is an averagegrayscale value of a target region of a target image, wherein the targetimage has a larger size than the dithering mask, and wherein thedithering mask is replicated to cover the target image.
 19. One or morecomputer-readable non-transitory storage media embodying software thatis operable when executed to: determine that a target grayscale value pfor a frame falls within one of a plurality of predetermined grayscaleranges; compute, based on the target grayscale value p, barycentricweights for a predetermined barycentric coordinate system associatedwith the predetermined grayscale ranges, wherein the barycentriccoordinate system is associated with vertices that each represents asubframe combination of zero or more subframe identifiers selected froma plurality of subframe identifiers; select, using the barycentricweights and threshold values associated with respective dots in adithering mask, a set of non-overlapping dot patterns from the ditheringmask corresponding to the vertices of the barycentric coordinate system,wherein the dots in the dithering mask satisfy a spatial stackingconstraint according to the threshold values associated with the dots;and generate a plurality of subframes corresponding to the plurality ofsubframe identifiers to represent the frame, wherein the plurality ofsubframes are generated based on the set of non-overlapping dot patternsand the subframe combination represented by each of the vertices.
 20. Asystem comprising: one or more non-transitory computer-readable storagemedia embodying instructions; and one or more processors coupled to thestorage media and operable to execute the instructions to: determinethat a target grayscale value p for a frame falls within one of aplurality of predetermined grayscale ranges; compute, based on thetarget grayscale value p, barycentric weights for a predeterminedbarycentric coordinate system associated with the predeterminedgrayscale ranges, wherein the barycentric coordinate system isassociated with vertices that each represents a subframe combination ofzero or more subframe identifiers selected from a plurality of subframeidentifiers; select, using the barycentric weights and threshold valuesassociated with respective dots in a dithering mask, a set ofnon-overlapping dot patterns from the dithering mask corresponding tothe vertices of the barycentric coordinate system, wherein the dots inthe dithering mask satisfy a spatial stacking constraint according tothe threshold values associated with the dots; and generate a pluralityof subframes corresponding to the plurality of subframe identifiers torepresent the frame, wherein the plurality of subframes are generatedbased on the set of non-overlapping dot patterns and the subframecombination represented by each of the vertices.